Extremal degree distance of bicyclic graphs - Chen, Shubo; Liu, Weijun; Xia, Fangli (Utilitas Mathematica, 2013)
For a graph G-(V,E),the degree distance of G is defined as DD(G)= Σ(dG(u))+ dG(v))dG(u,v)u,v⊆V(G) where dG(u)(or d(u))is the degree of the vertex u in G,and d gu,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.