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Cycles, The Degree Distance, And The Wiener Index, Daniel Gray, Hua Wang
Cycles, The Degree Distance, And The Wiener Index, Daniel Gray, Hua Wang
Department of Mathematical Sciences Faculty Publications
The degree distance of a graph G is D'(G)=(1/2)∑ni=1∑nj=1(di+dj)Li ,j, where di and dj are the degrees of vertices vi, vj ∈ V (G), and Li,j is the distance between them. The Wiener index is defined as W(G)=(1/2)∑ni=1 ∑nj-1Li, j. An elegant result (Gutman; Klein, Mihalic, Plavsic and Trinajstic) is known regarding their correlation, that D'(T)=4W(T)-n(n-1)for a tree T with n vertices. In …