The Laplacian spectral radius of bicyclic graphs with a given girth期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The Laplacian spectral radius of bicyclic graphs with a given girth

Authors:	Mingqing Zhai Guanglong Yu Jinlong Shu

Affiliation:	1. Department of Mathematics, East China Normal University, Shanghai, 200241, China;2. Department of Mathematics, Chuzhou University, Anhui, Chuzhou, 239012, China;3. Key Laboratory of Geographic Information Science, Ministry of Education East China Normal University, Shanghai, 200241, China

Abstract:	Let $? (n, g)$ be the class of bicyclic graphs on $n$ vertices with girth $g$ . Let $?_{1} (n, g)$ be the subclass of $? (n, g)$ consisting of all bicyclic graphs with two edge-disjoint cycles and $?_{2} (n, g) = ? (n, g) ? ?_{1} (n, g)$ . This paper determines the unique graph with the maximal Laplacian spectral radius among all graphs in $?_{1} (n, g)$ and $?_{2} (n, g)$ , respectively. Furthermore, the upper bound of the Laplacian spectral radius and the extremal graph for $? (n, g)$ are also obtained.

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