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2016 The minimum matching energy of bicyclic graphs with given girth
Hong-Hai Li, Li Zou
Rocky Mountain J. Math. 46(4): 1275-1291 (2016). DOI: 10.1216/RMJ-2016-46-4-1275


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 $g$.


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Hong-Hai Li. Li Zou. "The minimum matching energy of bicyclic graphs with given girth." Rocky Mountain J. Math. 46 (4) 1275 - 1291, 2016.


Published: 2016
First available in Project Euclid: 19 October 2016

zbMATH: 1347.05116
MathSciNet: MR3563182
Digital Object Identifier: 10.1216/RMJ-2016-46-4-1275

Primary: 05C35 , 05C50

Keywords: Bicyclic graph , Girth , matching energy

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium


Vol.46 • No. 4 • 2016
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