Extremal unicyclic graphs with respect to modified schultz index

Abstract

For a graph G= (V, E), the modified Schultz index of G is defined as S*(G)= Σ_{u,v}⊆V(G) (d_G(u)· dG(v))d_G(u,v) where dG(u) (or d(u)) is the degree of the vertex u of G, and dG(u, v) is the distance between u and v. Let u(n) be the set of unicyclic graph with n vertices. In this paper, we study the modified Schultz index of W (n) by introducing some transformations. Unicyclic graphs with the maximum and minimum modified Schultz index are determined.