Ordering of bicyclic graphs by matching energy

Abstract

Let $G$ be a simple graph of order $n$ and ${\mu }_1,{\mu }_2,\dots ,{\mu }_n$ be the roots of its matching polynomial. The matching energy is defined as the sum ${\sum }_{i=1}^n|{\mu }_i|$, which was introduced by Gutman and Wagner in 2012. In this paper, the graphs with the first five smallest matching energies among all bicyclic graphs for order $n>5$ are determined.

12 pages, 4 figures

Cited by in corpus (1)

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