Proyecciones (Antofagasta, On line)
https://www.revistaproyecciones.cl/index.php/proyecciones
<p><strong>PROYECCIONES</strong> publishes original papers from the following areas of mathematics:</p> <ul> <li>Algebra</li> <li>Dynamical Systems, Ergodic Theory and Ordinary Differential Equations</li> <li>General Topology</li> <li>Matrix Theory and Applications</li> <li>Operator Algebras and Operator Theory</li> <li>Partial Differential Equations</li> <li>Graph Theory</li> </ul> <p><strong>SPECIAL ISSUES</strong>: In addition to the regular issues, Projections publishes special issues with a focus on a specific topic of current interest, in homage to an important mathematician in an area of the journal, or dedicated to papers presented at a conference, commissioned by the Editorial Board and Guest Editors. Papers submitted to these special issues undergo the same rigorous peer review process as all other manuscripts. Inquiries regarding these special issues should be directed to the respective editors-in-chief.</p>Universidad Católica del Norte.enProyecciones (Antofagasta, On line)0717-6279<div id="deed-conditions" class="row"> <ul class="license-properties col-md-offset-2 col-md-8" dir="ltr"> <li class="license by"> <p><strong>Attribution</strong> — You must give <a id="appropriate_credit_popup" class="helpLink" tabindex="0" title="" href="https://creativecommons.org/licenses/by/4.0/deed.en" data-original-title="">appropriate credit</a>, provide a link to the license, and <a id="indicate_changes_popup" class="helpLink" tabindex="0" title="" href="https://creativecommons.org/licenses/by/4.0/deed.en" data-original-title="">indicate if changes were made</a>. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.<span id="by-more-container"></span></p> </li> </ul> </div> <div class="row"> <ul id="deed-conditions-no-icons" class="col-md-offset-2 col-md-8"> <li class="license"><strong>No additional restrictions</strong> — You may not apply legal terms or <a id="technological_measures_popup" class="helpLink" tabindex="0" title="" href="https://creativecommons.org/licenses/by/4.0/deed.en" data-original-title="">technological measures</a> that legally restrict others from doing anything the license permits.</li> </ul> </div>Outdegree equitable domination number of certain graph operators
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6275
<p>For a vertex <em>u</em> in the dominating set <em>D</em> of a graph <em>G</em>, the number of edges from <em>u</em> to <em>V-D</em> is called the outdegree of <em>u </em>with respect to <em>D</em>, <em>d°<sub>D, G</sub>(u)</em>. A dominating set <em>D </em>is called the outdegree equitable dominating set if the absolute value of the differences of outdegrees of any two vertices in <em>D</em> is at most one. The minimum cardinality of an outdegree equitable dominating set of <em>G</em> is called the outdegree equitable domination number of <em>G</em>, <em>γ<sub>oe</sub>(G)</em>. In this paper, we study the outdegree equitable domination number of certain graph operators such as complement, double graph, mycielskian and subdivision of graph.</p>
ArtículosOutdegree equitable dominating setOutdegree equitable domination number05C6905C99MathematicsThasneem T. R.Manju K. Menon
Copyright (c) 2024 Thasneem T R, Manju K Menon
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2024-08-262024-08-261037105310.22199/issn.0717-6279-6275On gr-n-submodules of graded modules over graded commutative rings
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6222
<p>Let G be a group with identity e. Let ℜ be a G-graded commutative ring, ℑ be a graded ℜ -module. In this paper, we introduce and study the concept of graded n-submodules of ℑ. We obtain many results concerning graded n-submodules. Some characterizations of graded n-submodules and their homogeneous components are given. A proper graded submodule U of ℑ is said to be a graded n-submodule if whenever r ∈ h(ℜ), m ∈ h(ℑ) with rm ∈ U and r ∉ Gr(Ann<sub>ℜ</sub>(ℑ)), then m ∈ U.</p>
Artículosgradedn-submodulesgraded n-idealsgraded prime sub-modules13A0216W50graded rings and graded modulesMariam Al-AzaizehKhaldoun Falah Al-Zoubi
Copyright (c) 2024 Khaldoun Falah Al-Zoubi, Mariam Al-Azaizeh
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2024-09-122024-09-121191120510.22199/issn.0717-6279-6222Notes on multiplicative generalized (σ, τ )-reverse derivations with Lie ideals of semiprime ∗-rings
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6189
<p>This article is devoted to investigation into the notion of multiplicative generalized(σ,τ)-reverse derivations associated with(σ,τ)-reverse derivations of semiprime∗-rings is characterized. The action of these derivations on∗-Lie ideals of semiprime∗-rings is also consideration. Moreover, the commutativity of semiprime∗-rings ad-mitting multiplicative generalized(σ,τ)-reverse derivations associated with(σ,τ)-reverse derivations satisfying certain algebraic identitieson∗-Lie ideals is explored.</p>
Artículosgeneralized(σ,τ)-reverse derivationssemiprime∗-rings∗-Lie idealmultiplicative generalized(σ,τ)-reverse derivations16W2516W1016N6016U80Mehsin Jabel Atteya
Copyright (c) 2024 Mehsin Atteya
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2024-09-122024-09-121173118910.22199/issn.0717-6279-6189Existence of mild solutions for non-instantaneous impulsive ξ-Caputo fractional integro-differential equations
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6282
<p><span class="fontstyle0">The aim of this paper is to investigate the existence of mild solutions for a nonlocal </span><span class="fontstyle2">ξ</span><span class="fontstyle0">-Caputo fractional non-instantaneous impulses semilinear integro-differential equation in a Banach space. The proofs are based on some fixed point theorems for condensing maps. As an application, an example is given to illustrate our theoretical results.</span> </p>
Artículosξ-Caputo fractional derivativeξ-fractional integralC0-semigroupmeasure of noncompactness34A0834A3747D06MathematicsWalid BenhaddaM'hamed ElomariAli El mfadelAbderrazak Kassidi
Copyright (c) 2024 Walid Benhadda, M'hamed Elomari, Ali El mfadel, Abderrazak Kassidi
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2024-09-122024-09-121207122810.22199/issn.0717-6279-6282Stability and boundedness of solutions of certain Lienard-type non-autonomous differential equations
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6155
<p>In this paper, the Liénard-type non-autonomous nonlinear differential equation</p> <p>ẍ+ p(t)f(x, ẋ) ẋ + q(t)g(x) = ϕ(t, x, ẋ)</p> <p>is investigated for uniform exponential asymptotic stability of solutions when ϕ(t, x, ẋ) ≡ 0, and uniform ultimate boundedness of solutions when ϕ(t, x, ẋ) ≠ 0, using the Lyapunov’s direct method</p>
ArtículosStability of solutionsBoundedness of solutionsNon-autonomous Lyapunov’s direct methodLiénard-type differential equations34D2034C11ordinary differential equationAbdullai AbdurasidA. L. OlutimoM. O. Omeike
Copyright (c) 2024 Abdullai Abdurasid, Olutimo A.L., M. O. Omeike
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2024-06-172024-06-1787388210.22199/issn.0717-6279-6155Results on super edge magic deficiency of some well-known classes of finite graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6329
<p>A graph Ω(Λ, Γ) is considered super edge magic if there exists a bijective function ϕ:Λ(Ω)∪Γ(Ω)→ {1, 2, 3, …,|Λ(Ω)|+|Γ(Ω)|} such that ϕ(τ<sub>1</sub>)+(τ<sub>1</sub>τ<sub>2</sub>)+ ϕ(τ<sub>2</sub>) is a constant for every edge τ<sub>1</sub>τ<sub>2 </sub>∈ Γ(Ω), and ϕ(Λ(Ω))= {1, 2, 3, …,|Λ(Ω)|}. Furthermore, the super edge magic deficiency of a graph Ω, denoted as μ<sub>s</sub> (Ω), is either the minimum non-negative integer η such that Ω∪ηK<sub>1</sub> is a super edge magic graph or +∞ if such an integer η does not exist. In this paper, we investigate the super edge magic deficiency of certain families of graphs.</p>
Artículosdegree splitting grap jellyfish graph jewel graphquadrilateral snake graphsuper edge magic graphsuper edge magic deficiencyshadow graphsplitting graph05C78Graph TheoryMuhammad ImranMurat CancanMuhammad NadeemMuhammad Faisal Nadeem
Copyright (c) 2024 Muhammad Imran, Murat Cancan, Muhammad Nadeem, Muhammad Faisal Nadeem
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2024-08-262024-08-261075109610.22199/issn.0717-6279-6329On graded pseudo 2-prime ideals
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5394
<p>In this paper, we study graded pseudo 2-prime ideals of graded commutative rings with nonzero identities. Let G be a commutative additive monoid with an identity element 0, and R=⊕<sub>g∈G</sub> R<sub>g </sub>be a commutative graded ring with a nonzero identity element. A proper graded ideal I of R is said to be a graded pseudo 2-prime ideal if whenever ab ∈ I for some homogeneous elements a,b ∈ R, then a²ⁿ ∈ Iⁿ or b²ⁿ ∈ Iⁿ for some n ∈ ℕ. Besides giving many properties of graded pseudo 2-prime ideals, we characterize graded almost valuation domains in terms of our new concept.</p>
Artículosgraded pseudo 2-prime ideal graded valuation domainalmost valuation domaingraded 2-prime ideal13A1513A0216W50Anass AssarrarNajib MahdouMuroj Al-ShboulÜnsal TekïrSuat Koç
Copyright (c) 2024 Anass Assarrar, Najib Mahdou, Muroj Al-Shboul, Unsal Tekir, Suat Koç
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2024-05-142024-05-1463164810.22199/issn.0717-6279-5394Singularity of cycle-spliced signed graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6376
<p>We consider the adjacency spectrum of cycle-spliced signed graphs (CSSG), i.e., signed graphs whose blocks are (independent) signed cycles. For a signed graph Σ, the nullity η(Σ) is the multiplicity of the 0-eigenvalue. The adjancency spectrum of cycle-spliced (signed) graphs is studied in the literature for the relation between the nullity η and the cyclomatic number c, in particular, it is known that 0≤η(Σ) ≤ c(Σ)+1. In this paper, nonsingular cycle-spliced bipartite signed graphs are characterized. For cycle-spliced signed graphs Σ having only odd cycles, we show that η(Σ) is 0 or 1. Finally, we compute the nullity of CSSGs consisting of at most three cycles.</p>
ArtículosNullityCycle-spliced bipartite signed graphscyclomatic number05C0505C50Linear algebra.Suliman KhanAdriana Ciampella
Copyright (c) 2024 Adriana Ciampella, Suliman Khan
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2024-06-172024-06-1784987110.22199/issn.0717-6279-6376The edge geodetic fault tolerant domination number of a graph
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6387
<p>For a connected graph G = (V, E), a set F⊆V is said to be an edge geodetic fault tolerant dominating set of G if F is both edge geodetic set and fault tolerant dominating set of G. The minimum cardinality of an edge geodetic fault tolerant dominating set of G is called the edge geodetic fault tolerant domination number of G and is denoted by γ<sub>geft</sub>(G). The edge geodetic fault tolerant domination number of certain classes of graphs are determined. It is shown that for each pair of integers 3 ≤a < b, there exists a connected graph G such that γ(G) = a, γ<sub>ge</sub> (G)= b and γ<sub>geft</sub>(G) = a + b-1, where γ(G), <sub>ge</sub> γ(G) and γ<sub>geft</sub>(G) are the domination number, edge geodetic domination number and edge geodetic fault tolerant domination number of G respectively.</p>
Artículosedge geodetic fault tolerant domination number, fault tolerant domination number, edge geodetic number, domination number, geodetic fault tolerant domination numberGraph TheoryDistance in graphStalin D.John Johnson
Copyright (c) 2024 Dr.D.Stalin, Dr.J.John
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2024-08-262024-08-261055107310.22199/issn.0717-6279-6387Homeomorphisms of the real line with singularities
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6381
<p>Given a real number a ≠ 0, we consider the set of homeomorphisms f: <strong>R</strong>\{0}→ <strong>R</strong> \{a} where{(x, y):x=0}is a vertical asymtote, {(x, y):y=a} is a horizontal asymtote and f is strictly increasing in each connected component (−∞,0) and (0,+∞). In this context, similar to circle homeomorphisms, all possible dynamics are shown. It is established the relationship between existence of periodic orbits and the limit sets. Also, whenever f<sup>−n</sup>(0) ≠a for all n ∈ <strong>N</strong>, then the non-existence of periodic orbits leads to a non-trivial limit set, which is either the whole line <strong>R</strong> or perfect and nowhere dense. It is shown a notion of separation of points that leads to transitivity</p>
ArtículosHomeomorphismsDiscontinuitiesInvariant compact/non-compact setsPeriodic orbitsTransitivityFractals37C8337E05Dynamical SystemsJean GiraldoLuis Bladismir Ruiz LealSergio Muñoz
Copyright (c) 2024 Sergio Muñoz, Luis Bladismir Ruiz Leal, Jean Giraldo
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2024-09-122024-09-121229125210.22199/issn.0717-6279-6381Stability and boundedness criteria for certain second-order nonlinear neutral stochastic functional differential equations
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6146
<p>This paper presents stochastic stability and stochastic boundedness to certain second-order nonlinear neutral stochastic differential equations. The second-order differential equation is weakened to a neutral stochastic system of first-order equations and used together with a second-order quadratic function to obtain perfect Lyapunov-Krasovskii functional. This functional is adapted and applied to obtain criteria on the nonlinear functions to ensure novel results on stochastic stability and stochastic asymptotic stability of the zero solution. Furthermore, when the forcing term is nonzero, fresh results on stochastic boundedness and uniform stochastic boundedness of solutions are obtained. The results of this paper are original, new, essentially improving, complementing, and simplifying several related ones in the literature. Two special cases of the theoretical results are supplied to demonstrate the applicability of the hypothetical results.</p>
ArtículosSecond-orderdifferential equationsnonlinear neutral stochasticuniform stabilityuniform boundedness34K1234K2034K4034K50Differential equationsAdeleke Timothy AdemolaShiping WenYuming FengWei ZhangLeszek Rutkowski
Copyright (c) 2024 Adeleke Timothy Ademola, S Wen, Y Feng, W Zhang, L Rutkowski
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2024-08-262024-08-26985100910.22199/issn.0717-6279-6146A characterization of σ-prime rings involving generalized derivations
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6412
<p>This paper’s major goal is to work on commutativity of σ-prime rings with second kind involution σ, involving generalized derivation satisfy the certain differential identities. Finally, we provide some examples to demonstrate that the conditions assumed in our results are not unnecessary</p>
Artículosσ-prime ringderivationinvolutiongeneralized derivation16N6016W25MathematicsArshad MadniMuzibur Rahman MozumderWasim AhmedAbu Zaid Ansari
Copyright (c) 2024 Wasim Ahmed, Md. Arshad Madni, Muzibur Rahman Mozumder, Abu Zaid Ansari
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2024-06-242024-06-2496598310.22199/issn.0717-6279-6412A note on P-Sasakian manifolds satisfying certain conditions
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6158
<p>In the present paper, we have studied the curvature tensors of PSasakian manifold. For a P-Sasakian manifold, W<sub>1</sub> ·S = 0, W<sub>1</sub> ·Z = 0 and W<sub>9</sub> · W<sub>1</sub> = 0 cases are considered. According these cases, PSasakian manifolds have been characterized such as η-Einstein and Einstein. In addition, we research W<sub>1</sub>-flat and W<sub>9</sub>-flat for a PSasakian manifold. The results are interesting and give an idea about the geometry of P-Sasakian manifold.</p>
ArtículosP-Sasakian manifoldη -Einstein manifoldW₁ curvature tensor53C1553C25.Pakize UygunMehmet Atçeken
Copyright (c) 2024 pakize uygun, Mehmet Atceken
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2024-06-192024-06-1989991010.22199/issn.0717-6279-6158A study on deg-centric graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6174
<p>The deg-centric graph of a simple, connected graph G, denoted by G<sub>d</sub>, is a graph constructed from G such that, V(G<sub>d</sub>) = V(G) and E(G<sub>d</sub>) = {v<sub>i</sub>v<sub>j</sub>: d<sub>G</sub>(v<sub>i</sub>,v<sub>j</sub>) ≤ deg<sub>G</sub>(v<sub>i</sub>)}. In this paper, the concepts of deg-centric graphs and iterated deg-centrication of a graph are introduced and discussed.</p>
ArtículosDistanceeccentricitydeg-centric graphsiterated deg-centric graphdeg-centrication process05C0705C12Timmy Tomy ThalavayalilJohan KokSudev Naduvath
Copyright (c) 2024 Sudev Naduvath, Timmy, Johan
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2024-06-242024-06-2491192610.22199/issn.0717-6279-6174Fixed point and stability of nonlinear differential equations with variable delays
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6374
<p>In this paper, we study the stability of a generalized nonlinear differential equation with variable delays via fixed point theory. An asymptotic stability theorem with sufficient conditions is proved, which improves and generalizes some previous results. Two examples are given to illustrate our results.</p>
ArtículosDifferential equationsStabilityFixed pointVariable delaysMackey--Glass equation34G2034K2034K2547H10MathematicsAbdelhafid Younsi
Copyright (c) 2024 Abdelhafid younsi
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2024-06-172024-06-1781382510.22199/issn.0717-6279-6374Uniform stability, boundedness and square integrability for non-autonomous third-order neutral differential equations with delay
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6286
<p>The work in this article provides literature with some results concerning the exponential stability, the boundedness and the square integrability of solutions for some non autonomous equations of third order supplied with delay and neutral parameters. The main tool used in this work is the second method of Lyapunov. The article is finished by giving a concrete example that ensure the application of the obtained results.</p>
ArtículosLyapunov functionaldifferential equations of third orderexponential stabilitysquare integrability34Dxx34D2034D23Differential EquationsMebrouk RahmaneFatima Abdellaoui
Copyright (c) 2024 Mebrouk Rahmane, Fatima Abdellaoui
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2024-06-172024-06-1782784710.22199/issn.0717-6279-6286An optimization model for fuzzy nonlinear programming with Beale's conditions using trapezoidal membership functions
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5468
<p>Non-linear Programming (NLP) is an optimization technique for determining the optimum solution to a broad range of research issues. Many times, the objective function is non-linear, owing to various economic behaviors such as demand, cost, and many others. Since the appearance of Kuhn and Tucker's fundamental theoretical work, a general NLP problem can be resolved using many methods to find the optimum solution. In this chapter, a fuzzy mathematical model based on Beale's condition is proposed to address NLP with inequality constraints in terms of fuzziness. Furthermore, the model demonstrates how quadratic programming problems can be solved using membership functions. The model also describes three stages: that is, mathematical formulation, computational procedures, and numerical illustration with comparative analysis. Likewise, the model illustrates the considered problem using two distinct approaches, namely membership functions (MF) and robust ranking index. Finally, the comparison analysis provides detailed results and discussion that justify the optimal outcome in order to address the vagueness of certain NLPPs.</p>
ArtículosNonlinear optimization – Fuzzy nonlinear programming problem – Beale’s conditions with fuzziness - Trapezoidal fuzzy membership functions.Operations ResearchFuzzy set theoryNonlinear programmingFuzzy optimization techniquesApplied MathematicsPalanivel KaliyaperumalMuralikrishna P.
Copyright (c) 2024 Palanivel Kaliyaperumal, Muralikrishna P
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2024-04-052024-04-0542544610.22199/issn.0717-6279-5468On graded 1 -absorbing δ -primary ideals
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6190
<p>Let G be an abelian group with identity 0 and let R be a commutative graded ring of type G with nonzero unity. Let I(R) be the set of all ideals of R and let δ: I(R)⟶I(R) be a function. Then, according to (R. Abu-Dawwas, M. Refai, Graded δ-Primary Structures, Bol. Soc. Paran. Mat., 40 (2022), 1-11), δ is called a graded ideal expansion of a graded ring R if it assigns to every graded ideal I of R another graded ideal δ(I) of R with I ⊆ δ(I), and if whenever I and J are graded ideals of R with J ⊆ I, we have δ (J) ⊆ δ(I). Let δ be a graded ideal expansion of a graded ring R. In this paper, we introduce and investigate a new class of graded ideals that is closely related to the class of graded δ-primary ideals. A proper graded ideal I of R is said to be a graded 1-absorbing δ-primary ideal if whenever nonunit homogeneous elements a,b,c ∊ R with abc ∊ I, then ab ∊ I or c ∊ δ(I). After giving some basic properties of this new class of graded ideals, we generalize a number of results about 1-absorbing δ-primary ideals into these new graded structure. Finally, we study the graded 1-absorbing δ-primary ideals of the localization of graded rings and of the trivial graded ring extensions.</p>
Artículosgraded 1-absorbing prime idealgraded 1-absorbing δ -primary idealgraded δ -primary idealtrivial graded ring extensionAlgebraRashid Abu-DawwasAnass AssarrarJebrel M HabebNajib Mahdou
Copyright (c) 2024 Rashid Abu-Dawwas, Anass Assarrar, Jebrel M Habeb, Najib Mahdou
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2024-05-022024-05-0257158610.22199/issn.0717-6279-6190Induced Dominating Sequence and ESD Graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6179
<p>A vertex subset D of a graph G = (V,E) is said to be a dominating set if every vertex in G is either in D or adjacent to some vertex in D. The minimum cardinality of such a set is the domination number, which is denoted as γ(G). In this paper, we define a sequence associated with the domination concept in graphs and studied the basic properties of the sequence in terms of various parameters of graphs. Using this sequence we order the vertices of a dominating set according its significance and propose Equally Significant Dominating (ESD) graphs. We also introduced domination related topological indices and compute their lower bounds for trees, unicyclic graphs and bicyclic graphs. All the graphs attaining the bounds are characterized.</p>
Artículosdominating setdomination number induced domination sequenceEqually significant dominating(ESD) graphinduced domination indexLiju AlexJohn Joy MulloorIndulal Gopalapilla
Copyright (c) 2024 Indulal Gopalapilla, Liju Alex, John Joy
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2024-06-192024-06-1994796410.22199/issn.0717-6279-6179Rainbow Mean Index of Some Classes of Graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6252
<p>In this article, we determine the rainbow mean index of cartesianproductG◻P<sub>n</sub>, where G is a regular graph;P<sub>m</sub>◻P<sub>n</sub>; W<sub>n</sub>◻K<sub>2</sub>;total graph of paths; chain of cycles and complete graphs; triangular treeand join graphs <sub>t</sub>C<sub>s</sub>∨K<sub>1</sub>.</p>
ArtículosRainbow Mean indexCartesian ProductTotal GraphJoin Graph05C0705C1505C78Applied MathematicsMaheswari K.Rajasekaran Ganapathy
Copyright (c) 2024 RAJASEKARAN G
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2024-08-262024-08-261011103610.22199/issn.0717-6279-6252On graded 2-absorbing primal ideals
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5695
<p>Let R be G-graded ring. In this paper, we introduce and devoted to the concept of graded 2-absorbing primal ideal of R which is a generalization of graded primal ideal. These ideals and their homogeneous components are given some features and characterizations.</p>
ArtículosGraded 2-absorbing primal idealGraded 2-absorbing idealGraded prime idealGraded primary ideal05C7513A1513A10Tamem Al-shormanMalik Bataineh
Copyright (c) 2024 Tamem Al-shorman, Malik Bataineh
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2024-05-202024-05-2069570610.22199/issn.0717-6279-5695On the eigenvalues of the distance signless Laplacian matrix of graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6247
<p>Let G be a connected graph and let D<sup>Q</sup>(G) be the distance signless Laplacian matrix of G with eigenvalues ρ<sub>1</sub>≥ ρ<sub>2</sub>≥…≥ ρ<sub>n</sub>. The spread of the matrix D<sup>Q</sup>}(G) is defined as s(D<sup>Q</sup>(G)) := max<sub>i,j</sub>| ρ<sub>i</sub>-ρ<sub>j</sub>| = ρ<sub>1</sub>- ρ<sub>n</sub>. We derive new bounds for the distance signless Laplacian spectral radius ρ<sub>1</sub> of G. We establish a relationship between the distance signless Laplacian energy and the spread of D<sup>Q</sup>(G). For a real number α ≠ 0, the graph invariant m<sub>α </sub>(G) is the sum of the α -th power of the distance signless Laplacian eigenvalues of G. Finally, we obtain various bounds for the graph invariant m<sub>α</sub>(G).</p>
ArtículosDistance signless Laplacian eigenvaluesdistance signless Laplacian energyspread05C50Spectral graph theoryAkbar JahanbaniHajar ShooshtariMohd Abrar Ul HaqShariefuddin Pirzada
Copyright (c) 2024 Akbar Jahanbani, Xuewu Zuo, Mohd Abrar Ul Haq, Shariefuddin Pirzada
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2024-09-122024-09-121253126710.22199/issn.0717-6279-6247On derivations over trivial extensions
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6040
<pre>In this paper, we investigate the structure of derivations over trivial extensions. We provide a detailed analysis of the structure of derivations on trivial extensions, the centre of trivial extensions, and the conditions for a trivial extension to be prime. Additionally, we examine the structure of derivations on trivial extensions when the underlying ring, $R$, is a prime ring, under the conditions of Herstein's Theorem, Posner's Theorem, and Bell's theorem.</pre>
ArtículosDerivationtrivial extensionprime ring16N6046J1016W25Brahim BoudineMohammed Zerra
Copyright (c) 2024 brahim boudine, Mohammed Zerra
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2024-04-032024-04-0345947210.22199/issn.0717-6279-6040Edge metric dimension of some Cartesian product of graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5770
<p>The edge metric dimension edim(G)of a connected graph G is the minimum cardinality of a set S of vertices such that each edge is uniquely determined by its distance from the vertices of the set S. In this work, the edge metric dimension of the prism over a graph G(G◻K<sub>2</sub>), cylinder graphs(C<sub>m</sub>◻P<sub>n</sub>)and torus graphs(C<sub>m</sub>◻ C<sub>n</sub>)are determined</p>
Artículosedge metric dimensionedge metric generator metric dimensioncartesian product of graphsMathematicsComputer scienceSaritha Chandran C.Reji T.
Copyright (c) 2024 Saritha Chandran C, Reji T
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2024-05-142024-05-1458761110.22199/issn.0717-6279-5770Further results on edge irregularity strength of some graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6175
<p>The focal point of this paper is to precisely ascertain the edge irregularity strength of various finite, simple, and undirected captivating graphs, including splitting graph, shadow graph, jewel graph, jellyfish graph, and $m$ copies of 4-pan graph.</p>
Artículosirregular assignmentirregularity strengthedge irregularity strengthsplitting graphshadow graphjewel graphjellyfish graph4-Pan graphMathematicsGraph TheoryMathematicsGraph TheoryMuhammad ImranMurat CancanMuhammad Faisal NadeemYasir Ali
Copyright (c) 2024 Muhammad Imran, Murat Cancan, Muhammad Faisal Nadeem, Yasir Ali
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2024-03-112024-03-1113315110.22199/issn.0717-6279-6175Group vertex magic labeling of some special graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5880
<p>For any additive abelian group $A$. Let $\mu$ be an element of $A$, a graph $G=(V,E)$ is said to be $A$-vertex magic graph if there exist a labeling function $f:V(G)\rightarrow A\setminus\{0\}$ such that $\omega(v)=\sum_{u\in N(v)} f(u)=\mu$ for any vertex $v$ of $G$, where $N(v)$ is the set of the open neighborhood of $v$. In this paper, we prove that the graphs such as wheel, Corona $C_{n}\odot mk$, subdivision of ladder and $t$-fold wheel for $t\neq n$ nor $n-2$ are $A$-vertex magic graphs. Also we prove that the subdivide wheel, helm and closed helm are $Z_{k}$-vertex magic graphs. However we prove that the triangular book and $t$-fold wheel for $t=n,n-2$ are group vertex magic graphs.<br><br></p>
ArtículosA-vertex magic Group vertex magicWeight of the vertex Subdivided wheel t-fold wheelHelmTriangular bookgraph labelingMohamed Basher
Copyright (c) 2024 mohamed basher basher
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2024-03-112024-03-1111913110.22199/issn.0717-6279-5880Antimagic Labeling for Some Snake Graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6005
<p>A graph with q edges is called antimagic if its edges can be labeled with 1, 2, 3, ..., q without repetition such that the sums of the labels of the edges incident to each vertex are distinct. In this paper we study antimagic labeling of double triangular snake, alternate triangular snake, double alternate triangular snake, quadrilateral snake, double quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake.</p>
ArtículosAntimagic labelingAntimagic graphSnake graphGraph TheoryGraph LabelingChirag BarasaraPalak Prajapati
Copyright (c) 2024 Chirag Barasara, Palak Prajapati
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2024-04-052024-04-0552153710.22199/issn.0717-6279-6005Further studies on circulant completion of graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6034
<p>A circulant graph C(n,S) is a graph having its adjacency matrix as a circulant matrix. It can also be intrepreted as a graph with vertices v<sub>0</sub>,v<sub>1</sub>,...,v<sub>n-1</sub> that are in one to one correspondence with the members of <strong>Z</strong><sub>n</sub> and with edge set {v<sub>i</sub>v<sub>j</sub>:i-j ∈ S}, where S known as the connection set or symbol, is a subset of non-identity members of <strong>Z</strong><sub>n</sub> that is closed under inverses. This work extends the study of circulant completion and general formulae for calculating circulant completion number in two different perspectives, one in terms of circulant span and the other in terms of adjacency matrix.</p>
Artículoscirculant completioncirculant completion graphcirculant spancirculant labellingΦ-completion?-diagobal modulo n?-traceGraph TheoryTony AntonySudev Naduvath
Copyright (c) 2024 Sudev Naduvath, Toby
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2024-05-262024-05-2676177310.22199/issn.0717-6279-6034A variant of Banach’s contraction principle in ordered Banach spaces
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6128
<p>In this article we establish a version of Banach’s contraction principle in ordered Banach spaces. This version is adapted to prove existence and uniqueness results for an integral equation or a boundary value problem depending on the derivative.</p>
ArtículosBanach’s contraction principleordered Banach spacespositive operators47H10 47H0747A1034B15MathematicsAbdelhamid Benmezai
Copyright (c) 2024 Abdelhamid Benmezai
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2024-05-022024-05-0255556910.22199/issn.0717-6279-6128Tight Bounds for the N₂-Chromatic Number of Graphs
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6117
<p>Let $G$ be a connected graph. A vertex coloring of $G$ is an $N_2$-vertex coloring if, for every vertex $v$, the number of different colors assigned to the vertices adjacent to $v$ is at most two. The $N_2$-chromatic number of $G$ is the maximum number of colors that can be used in an $N_2$-vertex coloring of $G$. In this paper, we establish tight bounds for the $N_2$-chromatic number of a graph in terms of its maximum degree and its diameter, and characterize those graphs that attain these bounds.</p>
ArtículosVertex coloring$N_2$-vertex coloring$N_2$-chromatic numbermaximum degreediameterGraph TheoryGraph TheoryArnold A. EniegoIan June GarcesJose B. Rosario
Copyright (c) 2024 Ian June Garces
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2024-03-112024-03-1124726310.22199/issn.0717-6279-6117