Weighted Szeged Index of Graphs


  • K. Pattabiraman Department of Mathematics, Annamalai University, Annamalainagar, India
  • P. Kandan Department of Mathematics, Annamalai University, Annamalainagar, India


The weighted Szeged index of a connected graph G is dened
as Szw(G) = Σe=uv 2E(G)(dG(u) + dG(v))nGu(e) nGv(e); where nGu (e) is the number of vertices of G whose distance to the vertex u is less than the distance to the vertex v in G: In this paper, we have obtained the weighted Szeged index Szw(G) of the splice graph S(G1;G2; y; z) and link graph L(G1;G2; y; z).


[1] A. R. Ashrafi, A. Hamzeh and S. Hossein-zadeh. Calculation of some topological indices of splices and link of graphs, J. Appl. Math. and Inf. 29(1-2)(2011), 327 - 335.

[2] M. Azar. A note on vertex-edge Wiener indices of graphs, Iranian Journal of Mathematical Chemistry 7(1)(2016), 11-17.

[3] A. T. Balaban (Ed.). Chemical Applications of Graph Theory, Academic Press, London (1976).

[4] T. Doslic. Splices, links and their degree-weighted Wiener polynomials, Graph Theory Notes New York, 48(2005), 47-55.

[5] A. Graovac, I. Gutman and D. Vukicevic (Eds.). Mathematical Methods and Modelling for Students of Chemistry and Biology, Hum Copies Ltd., Zagreb, (2009).

[6] I. Gutman. Introduction to Chemical Graph Theory, Faculty of Science, Kragujevac, (2003) (in Serbian).

[7] I. Gutman (Ed.). Mathematical Methods in Chemistry, Prijepolje Museum, Prijepolje, (2006).

[8] M. A. Hosseinzadeh, A. Iranmanesh and T. Doslic. On The Narumi-Katayama Index of Splice and Link of graphs, Electronic Notes in Discrete Mathematics 45(2014), 141-146.

[9] A. Ilic and N. Milosavljevic. The Weighted vertex PI index, Mathematical and Computer Modeling 57(3-4)(2013), 623-631.

[10] K. Pattabiraman and P. Kandan. Weighted PI index of corona product of graphs, Discrete Math. Algorithm Appl. 6(4)(2014), 1450055.

[11] K. Pattabiraman and P. Kandan. Weighted Szeged indices of some graph operations, Transactions on Combinatorics 5(1)(2016), 25-35.

[12] K. Pattabiraman, S. Nagarajan and M. Chandrasekharan. Weighted Szeged index of generalized hierarchical product of graphs, Gen. Math. Notes 23(2)(2014), 85-95.

[13] K. Pattabiraman and P. Kandan. On Weighted PI index of graphs, Electronic Notes in Discrete Mathematics 53(2016), 225-238.

[14] R.Sharafdini and I. Gutman. Splice graphs and their topological indices, Kragujevac J. Sci. 35(2013), 89-98.

[15] Z. Yarahmadi and G.H.Fath-Tabar. The Wiener, Szeged,PI, vertex PI, the First and Second Zagreb indices of N-branched phenylacetylenes Dendrimers, MATCH Communications in
Mathematical and in Computer Chemistry 65(2011), 201-208.

[16] Z. Yarahmadi. Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers, Iranian Journal of Mathematical Chem-
istry 1(2)(2010), 105-110.