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The Algebraic Connectivity of Graphs with Given Matching Number

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Abstract

The algebraic connectivity of a graph is the second smallest eigenvalue of the associated Laplacian matrix. In this paper, we not only characterize the extremal graphs with the maximal algebraic connectivity among all graphs of order n with given matching number, but also determine the extremal tree with the maximal algebraic connectivity among all trees of order n with given matching number.

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Authors and Affiliations

  1. School of Mathematical Sciences, Jiangsu Normal University, Xuzhou, 221116, People’s Republic of China

    Bao-Xuan Zhu

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  1. Bao-Xuan Zhu
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Correspondence to Bao-Xuan Zhu.

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Supported partially by Key Project of Chinese Ministry of Education (No.212098), a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions and Natural Science Foundation of Xuzhou Normal University (No.11XLR30).

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Zhu, BX. The Algebraic Connectivity of Graphs with Given Matching Number. Graphs and Combinatorics 29, 1989–1995 (2013). https://doi.org/10.1007/s00373-012-1206-7

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  • DOI: https://doi.org/10.1007/s00373-012-1206-7

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