Cycles, the Degree Distance, and the Wiener Index

Daniel Gray, Hua Wang

Department of Mathematical Sciences, Georgia Southern University, Statesboro, USA.
Department of Mathematics, University of Florida, Gainesville, USA.

DOI: 10.4236/ojdm.2012.24031                

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.

Keywords

Degree Distance; Wiener Index; Cacti

Conflicts of Interest

The authors declare no conflicts of interest.

References

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