Extremal degree distance of bicyclic graphs

Abstract

For a graph G-(V,E),the degree distance of G is defined as DD(G)= Σ(d_G(u))+ d_G(v))d_G(u,v){u,v}⊆V(G) where d_G(u)(or d(u))is the degree of the vertex u in G,and d _g{u,v)is the distance between u and v. Let B(n)be the set of bicyclic graph with n vertices. In this paper,we study the degree distance of B(n)by introducing grafting transformations,the lower bounds for DD(G)are determined. The corresponding extremal graphs are characterized as well.