Irregularity indices for line graph of Dutch windmill graph
Keywords:Dutch Windmill graph, Irregularity indices
Among topological descriptors topological indices are significant and they have a conspicuous role in chemistry. Dutch Windmill graph Dxy can be obtain by taking x copies of cycle Cy with a vertex in common. In this paper, we will compute some irregularity índices that are useful in quantitative structure activity relationship for Line Graph of Dutch Windmill graph.
M. Ajmal, W. Nazeer, M. Munir, S. M. Kang, and C. Y. Jung, “The M-polynomials and topological indices of generalized prism network”, International journal of mathematical analysis, vol. 11, pp. 293–303, 2017, doi: 10.12988/ijma.2017.7118
D. Amić, D. Bešlo, B. Lučić, S. Nikolić, and N. Trinajstić, “The vertex-connectivity index revisited”, Journal of chemical information and computer sciences, vol. 38, no. 5, pp. 819–822, Aug. 1998, doi: 10.1021/ci980039b
B. Bollobás, P. Erdös, “Graphs of extremal weights”, Ars combinatoria, vol. 50, pp. 225-233, 1998.
B. Chaluvaraju, H. S. Boregowda, and S. A. Diwakar, “Hyper-Zagreb indices and their polynomials of some special kinds of windmill graphs”, International journal of advances in mathematics, vol. 4, pp. 21-32, 2017. [On line]. Available: https://bit.ly/2YSiyqg
A. A. Dobrynin, R. Entringer, and I. Gutman, “Wiener Index of Trees: theory and applications”, Acta applicandae mathematicae, vol. 66, no. 3, pp. 211–249, 2001, doi: 10.1023/A:1010767517079
P. Erdöus, “Problems and results in combinatorial analysis and graph theory”, Annals of discrete mathematics, vol. 38, pp. 81–92, 1988, doi: 10.1016/s0167-5060(08)70773-8
O. Favaron, M. Mahéo, and J. F. Saclé, “Some eigenvalue properties in graphs (conjectures of Graffiti — II)”, Discrete mathematics, vol. 111, no. 1-3, pp. 197–220, Feb. 1993, doi: 10.1016/0012-365x(93)90156-n
W. Gao, J. L. G. Guirao, M. Abdel-Aty, and W. Xi, “An independent set degree condition for fractional critical deleted graphs”, Discrete & continuous dynamical systems - S, vol. 12, no. 4-5, pp. 877–886, 2019, doi: 10.3934/dcdss.2019058
W. Gao and M. R. Farahani, “Degree-based indices computation for special chemical molecular structures using edge dividing method”, Applied mathematics and nonlinear sciences, vol. 1, no. 1, pp. 99–122, Jan. 2016, doi: 10.21042/amns.2016.1.00009
W. Gao and M. R. Farahani, and L. Shi, “The forgotten topological index of some drug structures”, Acta medica mediterranea, vol. 32, no. 1, pp. 579-585, 2016. [On line]. Available: https://bit.ly/2AZShi3
W. Gao, W. Wang, D. Dimitrov, and Y. Wang, “Nano properties analysis via fourth multiplicative ABC indicator calculating”, Arabian journal of chemistry, vol. 11, no. 6, pp. 793–801, Sep. 2018, doi: 10.1016/j.arabjc.2017.12.024
W. Gao, W. Wang, and M. R. Farahani, “Topological indices study of molecular structure in anticancer drugs”, Journal of chemistry, vol. 2016, Art. ID-3216327, 2016, doi: 10.1155/2016/3216327
W. Gao, Y. Wang, W. Wang, and L. Shi, “The first multiplication atom-bond connectivity index of molecular structures in drugs”, Saudi pharmaceutical journal, vol. 25, no. 4, pp. 548–555, May 2017, doi: 10.1016/j.jsps.2017.04.021
W. Gao, H. Wu, M. K. Siddiqui, and A. Q. Baig, “Study of biological networks using graph theory”, Saudi journal of biological sciences, vol. 25, no. 6, pp. 1212–1219, Sep. 2018, doi: 10.1016/j.sjbs.2017.11.022
M. Ghorbani, and M. Ghazi, “Computing some topological indices of Triangular Benzenoid”, Digest journal of nanomaterials and biostructures, vol. 5, no. 4, pp. 1107-1111, 2010. [On line]. Available: https://bit.ly/2YUDdu6
C. K. Gupta, V. Lokesha, S. B. Shwetha, and P. S. Ranjini, “On the symmetric division deg index of graph”, Southeast Asian Bulletin of Mathematics, vol. 40, no. 1, 2016. [On line]. Available: https://bit.ly/2BtCTu8
I. Gutman, and K. C. Das, “The first Zagreb index 30 years after”, MATCH communications in mathematical and in computer chemistry, vol. 50, no. 1, pp. 83-92, 2004. [On line]. Available: https://bit.ly/2YpODHe
I. Gutman, B. Furtula, and C. Elphvick, “Three new/old vertex-degree based topological índices”, MATCH communications in mathematical and in computer chemistry, vol. 72, no. 3, pp. 617-632, 2014. [On line]. Available: https://bit.ly/2Yq185B
I. Gutman, and O. E. Polansky, Mathematical concepts in organic chemistry. Berlin: Springer-Verlag, 2012.
Y. Kwun, A. Virk, W. Nazeer, M. Rehman, and S. Kang, “On the multiplicative degree-based topological indices of silicon-carbon Si2C3-I[p,q] and Si2C3-II[p,q]”, Symmetry, vol. 10, no. 8, p. 320, Aug. 2018, doi: 10.3390/sym10080320
X. Li and I. Gutman, Mathematical aspects of Randić-type molecular structure descriptors. Čačak: University. of Kragujevac, 2006.
X. Li, and Y. Shi, “A survey on the Randić index”, MATCH communications in mathematical and in computer chemistry, vol. 59, no. 1, pp. 127-156, 2008. [On line]. Available: https://bit.ly/2YrVkbP
A. Miličević, S. Nikolić, and N.Trinajstić, “On reformulated Zagreb indices”, Molecular diversity, vol. 8, no. 4, pp. 393–399, 2004, doi: 10.1023/b:modi.0000047504.14261.2a
M. Munir, W. Nazeer, Z. Shahzadi, and S. Kang, “Some invariants of circulant graphs”, Symmetry, vol. 8, no. 11, p. 134, Nov. 2016, doi: 10.3390/sym8110134
M. Naeem, M. K. Siddiqui, J. L. G. Guirao, and W. Gao, “New and modified eccentric indices of octagonal grid omn”, Applied mathematics and nonlinear sciences, vol. 3, no. 1, pp. 209–228, 2018, doi: 10.21042/amns.2018.1.00016
S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstic, “The Zagreb indices 30 years after”, Croatica chemica acta, vol. 76, no. 2, pp. 113-124, 2003. [On line]. Available: https://bit.ly/3drifZ0
M. Randić, “Characterization of molecular branching”, Journal of the American Chemical Society, vol. 97, no. 23, pp. 6609–6615, Nov. 1975, doi: 10.1021/ja00856a001
T. Réti, R. Sharafdini, A. Dregelyi-Kiss, and H. Haghbin, “Graph irregularity indices used as molecular descriptors in QSPR studies”, MATCH Communications in Mathematical and in Computer Chemistry, vol. 79, no. 2, pp. 509-524, 2018. [On line]. Available: https://bit.ly/2YpajmT
D. Vukičević, D., and A. Graovac, “Valence connectivity versus Randić, Zagreb and modified Zagreb index: A linear algorithm to check discriminative properties of indices in acyclic molecular graphs”, Croatica chemica acta, vol. 77, no. 3, pp. 501-508, 2004. [On line]. Available: https://bit.ly/2V9Jfpr
H. Whitney, “A logical expansion in mathematics”, Bulletin of the American Mathematical Society, vol. 38, no. 8, pp. 572–580, Aug. 1932, doi: 10.1090/s0002-9904-1932-05460-x
H. Wiener, “Structural determination of paraffin boiling points”, Journal of the American Chemical Society, vol. 69, no. 1, pp. 17–20, Jan. 1947, doi: 10.1021/ja01193a005
K. Yang, Z. Yu, Y. Luo, Y. Yang, L. Zhao, and X. Zhou, “Spatial and temporal variations in the relationship between lake water surface temperatures and water quality - A case study of Dianchi Lake”, Science of the total environment, vol. 624, pp. 859–871, May 2018, doi: 10.1016/j.scitotenv.2017.12.119
How to Cite
Copyright (c) 2020 Mohanad A. Mohammed, Suad Younus A. AL-Mayyahi AL-Mayyahi, Abaid ur Rehman Virk, Hafiz Mutee ur Rehman
This work is licensed under a Creative Commons Attribution 4.0 International License.