Restricted detour polynomial of edge-identification of two wheel graphs

Abstract

The restricted detour distance D*(u, v) between two vertices u and v of G is the length of a longest u – v path P in G such that 〈V(P)〉 = P. The restricted detour polynomial of the graph G is denoted by D*(G; x) and defined as D*(G; x) = ∑u,vxD*(u,v). The restricted detour index dd*(G) of a connected graph G is the Wiener index with respect to restricted detour distance, that is dd*(G) = ∑u,v D*(u,v). In this paper, the restricted detour polynomial and restricted detour index of edge identification of two wheel graphs are obtained.