The Wiener Index of Unicyclic Graphs with Girth and the Matching Number

Ya-Hong Chen; Xiao-Dong Zhang

paper

The Wiener Index of Unicyclic Graphs with Girth and the Matching Number

arXiv:1102.5409

Abstract

In this paper, we investigate how the Wiener index of unicyclic graphs varies with graph operations. These results are used to present a sharp lower bound for the Wiener index of unicyclic graphs of order $n$ with girth and the matching number $β \geq \frac{3 g}{2}$ . Moreover, we characterize all extremal graphs which attain the lower bound.

15 pages