The Values of Eccentricity-Based Topological Indices of Diamond Graphs
Graph theory has been studied different areas such as information, mathematics and chemistry sciences. Especially, it has been the most important mathematical tools for the study the analysis of chemistry. A topological index has been a numerical descriptor of the molecular structure derived from the corresponding molecular graph, also it has used vulnerability of chemical graphs. The vulnerability of a graph has been the reliability of the graph after the disruption of some vertices or edges until breakdown. There are a lot of topological indices which have been defined. Furthermore, the diamond graphs have been defined recently. In this paper, exact formulas for the eccentricity-based topological indices of diamond graphs have been obtained.
 Wiener, H. 1947. Structrual determination of paraffin boiling points. Journal of the American Chemical Society, 69(1), 17-20.
 Dobrynin A. A., Entringer, R. , Gutman, I., 2001. Wiener index of trees: theory and applications. Acta Applicandae Mathematicae, 66 , 211–249.
 Todeschini R., Consonni, V. 2000. Handbook of Molecular Descriptors. Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim, 668s.
 Turacı, T. 2016. Zagreb Eccentricity Indices of Cycles Related Graphs. Ars Combinatoria, 125, 247-256.
 West, D.B. 1996. Introduction to Graph Theory, 2nd edition. Prentice Hall, Upper Saddle, River, 512s.
 Harary F., Buckley, F. 1989. Distance in Graphs. Addison-Wesley Publishing Company, 352s.
 Gallian, J.A. 2014. Graph labeling, Electronic Journal of Combinatorics, 17, (Dynamic Survey #DS6).
 Shulhany, M.A., Salman, A.N.M. 2015. Bilangan Terhubung Pelangi Graf Berlian. Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, UMS( 2015), 916–924.
 Hinding, N., Firmayasari, D., Basir, H., Bača, M. and Feňovčíková, A.S. 2017. On irregularity strength of diamond network. AKCE International Journal of Graphs and Combinatorics,Doi: 10.1016/j.akcej.2017.10.003
 Gupta, S, Singh, M., Madan, A.K. 2000. Connective eccentricity index: a novel topological descriptor for predicting biological activity. Journal of Molecular Graphics and Modelling, 18(1), 18–25.
 Sharma, V., Goswami, R., Madan, A.K. 1997. Eccentric connectivity index: A novel highly discriminating topological descriptor for structure–property and structure–activity studies. Journal of Molecular Graphics and Modelling, 37(2), 273–282.
 Gutman, I., Trinajstic, N. 1972 Graph theory and molecular orbitals. III. Total _-electron energy of alternant hydrocarbons. Chemical Physics Letters, 17, 535–538.
 Gutman, I., Ruscic, B., Trinajstic, N., Wilcox, C.F. 1975. Graph theory and molecular orbitals. XII. Acyclic polyenes. Journal of Chemical Physics, 62, 3399–3405.
 Vukicevic, D., Graovac, A. 2010. Note on the comparison of the first and second normalized Zagreb eccentricity indices. Acta Chimica Slovenica, 57, 524–528.
 Xu, X., Guo, Y. 2012. The Edge Version of Eccentric Connectivity Index. International Mathematical Forum, 7, 273-280.
 Odabas, Z.N. 2013. The Edge Eccentric Connectivity Index of Dendrimers, Journal of Computational and Theoretical Nanoscience, 10(4), 783-784.
 Berberler, Z.N., Berberler, M.E. 2016. Edge eccentric connectivity index of nanothorns. Bulgarian Chemical Communications, 48(1), 165-170.
 Turacı, T., Ökten, M. 2015. The Edge Eccentric Connectivity Index of Hexagonal Cactus Chains. Journal of Computational and Theoretical Nanoscience, 12(10), 3977-3980.
 Aslan, E. 2015. The Edge Eccentric Connectivity Index of Armchair Polyhex Nanotubes. Journal of Computational and Theoretical Nanoscience, 12(11), 4455-4458.
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