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Hosoya polynomial, Wiener and Hyper-Wiener indices of some regular graphs

Mohammad Reza Farahani
2020 Zenodo  
Let G be a graph. The distance d(u,v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as ( ) ( ) ( ) ( ) ( ) 2 {u,v} V G WW G d v u d v u , , . ∈ = + ∑ Also, the Hosoya polynomial was introduced by H. Hosoya and define ( ) ( ) ( ) , {u,v} V G , . d v u H G x x ∈ = ∑ In this paper, the Hosoya polynomial, Wiener index and
more » ... ner index and Hyper-Wiener index of some regular graphs are determined. Let G be a graph. The distance d(u,v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as ( ) ( ) ( ) ( ) ( ) 2 {u,v} V G WW G d v u d v u , , . ∈ = + ∑ Also, the Hosoya polynomial was introduced by H. Hosoya and define ( ) ( ) ( ) , {u,v} V G , . d v u H G x x ∈ = ∑ In this paper, the Hosoya polynomial, Wiener index and Hyper-Wiener index of some regular graphs are determined.
doi:10.5281/zenodo.3735657 fatcat:o2vdt356rrgmtdzs5u6nqwq2se