## Rocky Mountain Journal of Mathematics

### The minimum matching energy of bicyclic graphs with given girth

#### Abstract

The matching energy of a graph was introduced by Gutman and Wagner in 2012 and defined as the sum of the absolute values of zeros of its matching polynomial. Let $\theta (r,s,t)$ be the graph obtained by fusing two triples of pendant vertices of three paths $P_{r+2}$, $P_{s+2}$ and $P_{t+2}$ to two vertices. The graph obtained by identifying the center of the star $S_{n-g}$ with the degree~3 vertex $u$ of $\theta (1,g-3,1)$ is denoted by $S_{n-g}(u)\theta (1,g-3,1)$. In this paper, we show that, $S_{n-g}(u)\theta (1,g-3,1)$ has minimum matching energy among all bicyclic graphs with order $n$ and girth $g$.

#### Article information

Source
Rocky Mountain J. Math., Volume 46, Number 4 (2016), 1275-1291.

Dates
First available in Project Euclid: 19 October 2016

https://projecteuclid.org/euclid.rmjm/1476884583

Digital Object Identifier
doi:10.1216/RMJ-2016-46-4-1275

Mathematical Reviews number (MathSciNet)
MR3563182

Zentralblatt MATH identifier
1347.05116

#### Citation

Li, Hong-Hai; Zou, Li. The minimum matching energy of bicyclic graphs with given girth. Rocky Mountain J. Math. 46 (2016), no. 4, 1275--1291. doi:10.1216/RMJ-2016-46-4-1275. https://projecteuclid.org/euclid.rmjm/1476884583

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