TITLE:
Cycles, the Degree Distance, and the Wiener Index
AUTHORS:
Daniel Gray, Hua Wang
KEYWORDS:
Degree Distance; Wiener Index; Cacti
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.2 No.4,
November
1,
2012
ABSTRACT: The degree distance of a graph G is , where and are the degrees of vertices , and is the distance between them. The Wiener index is defined as . An elegant result (Gutman; Klein, Mihali?,, Plav?i? and Trinajsti?) is known regarding their correlation, that
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.