THE SIGMA INDEX OF GRAPH OPERATIONS

Yıl 2019, Cilt: 37 Sayı: 1, 155 - 162, 01.03.2019

Akbar Jahanbanı Süleyman Ediz

Öz

Let G be a graph of order n with vertices labeled as v1, v2, …, vn. Let di be the degree of the vertex vi, for i = 1, 2, …, n. The sigma index, which have been defined very recently, of G is (G) = ΣvivjE(G)(di  dj)2. In this paper, the sigma index of the Cartesian product, composition, join and disjunction of graphs are computed. We apply some of our results to compute the sigma index of some special graph classes.

Anahtar Kelimeler

Graph operations, sigma index, zagreb index.

Kaynakça

• [1] W. Gao, W. Wang, M. R. Farahani, Topological Indices Study of Molecu- lar Structure in Anticancer Drugs, Hindawi Publishing Corporation Journal of Chemistry, (2016), http://dx.doi.org/10.1155/2016/3216327.
• [2] I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83-92.
• [3] I. Gutman, N. Trinajstic´, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538.
• [4] I. Gutman, Degreebased topological indices, Croatica Chemica Acta, 86 (2013) 351-361.
• [5] I. Gutman, M. Togan, A. Yurttas, A. S. Cevik, I. N. Cangul, Inverse Problem for Sigma Index, MATCH Commun. Math. Comput. Chem. 79 (2018), 491-508.
• [6] Y. Huang. B. Liu, M. Zhang, On Comparing the variable Zagreb indices, MATCH Commun. Math. Comput. Chem. 63 (2010), 453-460.
• [7] W. Imrich, S. Klavzar, Product Graphs, Structure and Recognition, John Wiley Sons, New York, USA, 2000.
• [8] B. Liu, Z. You, A survey on comparing Zagreb indices, MATCH Commun. Math. Comput. Chem. 65 (2011), 581-593.
• [9] N. Jafari. Rad, A. Jahanbani, I. Gutman, Zagreb Energy and Zagreb Estrada Index of Graphs,MATCH Commun. Math. Comput. Chem, 79 (2018), 371-386.
• [10] M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, The Hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008), 1402-1407.
• [11] G. H. Shirdel, H. Rezapour, A. M. Sayadi, The Hyper-Zagreb Index of Graph Operations, Iranian Journal of Mathematical Chemistry, 2 (2013), 213- 220.
• [12] D. B. West, Introduction to Graph Theory, Second Edition, Prentice Hall, 2001.