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

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

2011-02-26

arxiv.org/abs/1102.5409v1

Mathematics

Combinatorics

15 pages

Scientific paper

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 $\beta\ge \frac{3g}{2}$. Moreover, we characterize all extremal
graphs which attain the lower bound.

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