Document Type

Article

Publication Date

10-2012

Publication Title

Open Journal of Discrete Mathematics

DOI

10.4236/ojdm.2012.24031

ISSN

2161-7643

Abstract

The degree distance of a graph G is D'(G)=(1/2)∑ni=1nj=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=1nj-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 this note, we extend this study for more general graphs that have frequent appearances in the study of these indices. In particular, we develop a formula regarding their correlation, with an error term that is presented with explicit formula as well as sharp bounds for unicyclic graphs and cacti with given parameters.

Comments

Article under the Creative Commons license "Attribution" (CC BY). Article obtained from the Open Journal of Discrete Mathematics.

Included in

Mathematics Commons

Share

COinS