The Values of Eccentricity-Based Topological Indices of Diamond Graphs

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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.

Anahtar kelimeler

Graph theory; Vulnerability; Eccentricity; Topological indices; Diamond graphs

Tam metin:



[1] Wiener, H. 1947. Structrual determination of paraffin boiling points. Journal of the American Chemical Society, 69(1), 17-20.

[2] Dobrynin A. A., Entringer, R. , Gutman, I., 2001. Wiener index of trees: theory and applications. Acta Applicandae Mathematicae, 66 , 211–249.

[3] Todeschini R., Consonni, V. 2000. Handbook of Molecular Descriptors. Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim, 668s.

[4] Turacı, T. 2016. Zagreb Eccentricity Indices of Cycles Related Graphs. Ars Combinatoria, 125, 247-256.

[5] West, D.B. 1996. Introduction to Graph Theory, 2nd edition. Prentice Hall, Upper Saddle, River, 512s.

[6] Harary F., Buckley, F. 1989. Distance in Graphs. Addison-Wesley Publishing Company, 352s.

[7] Gallian, J.A. 2014. Graph labeling, Electronic Journal of Combinatorics, 17, (Dynamic Survey #DS6).

[8] Shulhany, M.A., Salman, A.N.M. 2015. Bilangan Terhubung Pelangi Graf Berlian. Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, UMS( 2015), 916–924.

[9] 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

[10] 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.

[11] 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.

[12] Gutman, I., Trinajstic, N. 1972 Graph theory and molecular orbitals. III. Total _-electron energy of alternant hydrocarbons. Chemical Physics Letters, 17, 535–538.

[13] 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.

[14] Vukicevic, D., Graovac, A. 2010. Note on the comparison of the first and second normalized Zagreb eccentricity indices. Acta Chimica Slovenica, 57, 524–528.

[15] Xu, X., Guo, Y. 2012. The Edge Version of Eccentric Connectivity Index. International Mathematical Forum, 7, 273-280.

[16] Odabas, Z.N. 2013. The Edge Eccentric Connectivity Index of Dendrimers, Journal of Computational and Theoretical Nanoscience, 10(4), 783-784.

[17] Berberler, Z.N., Berberler, M.E. 2016. Edge eccentric connectivity index of nanothorns. Bulgarian Chemical Communications, 48(1), 165-170.

[18] Turacı, T., Ökten, M. 2015. The Edge Eccentric Connectivity Index of Hexagonal Cactus Chains. Journal of Computational and Theoretical Nanoscience, 12(10), 3977-3980.

[19] Aslan, E. 2015. The Edge Eccentric Connectivity Index of Armchair Polyhex Nanotubes. Journal of Computational and Theoretical Nanoscience, 12(11), 4455-4458.