Proyecciones (Antofagasta, On line) https://www.revistaproyecciones.cl/index.php/proyecciones <p align="justify">La revista&nbsp;Proyecciones. Journal of Mathematics es una publicación científica, sin fines de lucro, oficial de la Universidad Católica del Norte, Antofagasta, Chile. Fue fundada en 1982 y depende del Departamento de Matemáticas de la Universidad Católica del Norte.<br>Proyecciones. Journal of Mathematics edita un volumen con 5 números al año.</p> Universidad Católica del Norte. en-US Proyecciones (Antofagasta, On line) 0717-6279 On I- statistically ϕ-convergence https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4036 <p><em>In this paper we investigate the notion of I-statistical ϕ-convergence and introduce I<sub>S</sub>-ϕ limit points and I<sub>S</sub>-ϕ cluster points of real number sequence and also studied some of its basic properties.</em></p> Shyamal Debnath Chiranjib Choudhury Copyright (c) 2021 Shyamal Debnath, Chiranjib Choudhury http://creativecommons.org/licenses/by/4.0 2021-04-27 2021-04-27 40 3 593 604 10.22199/issn.0717-6279-4036 Some generalized results related to Fibonacci sequence https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4269 <p><em>Cassini's identity states that for the n<sup>th</sup> Fibonacci number F<sub>n+1</sub>F<sub>n-1</sub>-F<sub>n</sub><sup>2</sup>=(-1)<sup>n</sup>, We generalize Fibonacci sequence in terms of the number of sequences. Fibonacci sequence is the particular case of generating only one sequence. This generalization is used to generalize Cassini’s identity. Moreover we prove few more results which can be seen as generalized form of the results which hold for Fibonacci sequence.</em></p> Neeraj Kumar Paul Helen K. Saikia Copyright (c) 2021 Neeraj Kumar Paul, Helen K. Saikia http://creativecommons.org/licenses/by/4.0 2021-04-27 2021-04-27 40 3 605 617 10.22199/issn.0717-6279-4269 SD-prime cordial labeling of alternate k-polygonal snake of various types https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4015 <p><em>Let f : V (G) → {1, 2,..., |V (G)|} be a bijection, and let us denote S = f(u) + f(v) and D = |f(u) − f(v)| for every edge uv in E(G). Let f' be the induced edge labeling, induced by the vertex labeling f, defined as f' : E(G) → {0, 1} such that for any edge uv in E(G), f' (uv)=1 if gcd(S, D)=1, and f' (uv)=0 otherwise. Let e<sub>f' </sub>(0) and e<sub>f'</sub> (1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |e<sub>f'</sub> (0) − e<sub>f'</sub> (1)| ≤ 1 and G is SD-prime cordial graph if it admits SD-prime cordial labeling. In this paper, we have discussed the SD-prime cordial labeling of alternate k-polygonal snake graphs of type-1, type-2 and type-3.</em></p> Udayan Prajapati Anit Vantiya Copyright (c) 2021 Udayan Prajapati, Anit Vantiya http://creativecommons.org/licenses/by/4.0 2021-04-27 2021-04-27 40 3 619 634 10.22199/issn.0717-6279-4015 The edge-to-edge geodetic domination number of a graph https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4057 <p>Let G = (V, E) be a connected graph with at least three vertices. A set S Í E is called an edge-to-edge geodetic dominating set of G if S is both an edge-to-edge geodetic set of G and an edge dominating set of G. The edge-to- edge geodetic domination number ¡gee(G) of G is the minimum cardinality of its edge-to-edge geodetic dominating sets and any edge-to-edge geodetic dominating set of minimum cardinality is said to be a gee- set of G. Some general properties satisfied by this concept are studied. Connected graphs of size m?2 with edge-to-geodetic domination number 2 or m or m-1 are charaterized. We proved that if G is a connected graph of size m ? 3 and G­ is also connected,then 4 ?¡gee(G) + ¡gee(G­) ? 2m -2. Moreover we characterized graphs for which the lower and the upper bounds are sharp. It is shown that, for every pair of positive integers a and b with 2 ?a ? b, there exists a connected graph G with gee(G) = a and ¡gee(G) = b. Also it is shown that, for every pair of positive integers a and b with 2 &lt; a ? b, there exists a connected graph G with ¡e(G) = a and¡ gee(G) = b, where ¡e(G) is the edge domination number of G and gee(G) is the edge-to-edge geodetic number of G.</p> J. John V. Sujin Flower Copyright (c) 2021 J. John, V. Sujin Flower http://creativecommons.org/licenses/by/4.0 2021-04-27 2021-04-27 40 3 635 658 10.22199/issn.0717-6279-4057 On locating chromatic number of Möobius ladder graphs https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4170 <p>In this paper, we are dealing with the study of locating chromatic number of Möbius-ladders. We prove that Möbius-ladders M<sub>n</sub> with n even has locating chromatic number 4 if n≠6 and 6 if n=6.</p> Redha Sakri Moncef Abbas Copyright (c) 2021 Redha Sakri, Moncef Abbas http://creativecommons.org/licenses/by/4.0 2021-04-29 2021-04-29 40 3 659 669 10.22199/issn.0717-6279-4170 New types of locally connected spaces via clopen set https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4198 <p>In this paper, we define and study a new type of connected spaces called λ<sub>co</sub>-connected space. It is remarkable that the class of λ-connected spaces is a subclass of the class of λ<sub>co</sub>-connected spaces. We discuss some characterizations and properties of λ<sub>co</sub>-connected spaces, λ<sub>co</sub> components and λ<sub>co</sub>-locally connected spaces.</p> Ennis Rafael Rosas Rodriguez Sarhad Namiq Copyright (c) 2021 Ennis Rafael Rosas Rodriguez, Sarhad Namiq http://creativecommons.org/licenses/by/4.0 2021-04-27 2021-04-27 40 3 671 679 10.22199/issn.0717-6279-4198 Continuity in fuzzy bitopological ordered spaces https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4386 <p><em>The aim of the present paper is to introduce and study different forms of continuity in fuzzy bitopological ordered spaces. The concepts of different mappings such as pairwise fuzzy I -continuous mappings, pairwise fuzzy D -continuous mappings, pairwise fuzzy B -continuous mappings, pairwise fuzzy I -open mappings, pairwise fuzzy D -open mappings, pairwise fuzzy B -open mappings, pairwise fuzzy I -closed mappings, pairwise fuzzy D -closed mappings and pairwise fuzzy B -closed mappings have been introduced. Some of the basic properties and characterization theorems of these mappings have been investigated.</em></p> Runu Dhar Copyright (c) 2021 Runu Dhar http://creativecommons.org/licenses/by/4.0 2021-04-30 2021-04-30 40 3 681 696 10.22199/issn.0717-6279-4386