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<p>The algebraic connectivity of a graph is the second smallest eigenvalue of its Laplacian matrix. In this paper, we characterize all the extremal graphs with the maximal algebraic connectivity among all graphs with given order and induced matching number. Furthermore, for trees with given induced matching number, the first three values of the maximal algebraic connectivity and the corresponding extremal trees are also determined.</p>

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The algebraic connectivity of graphs with given induced matching number

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Ji-Ming Guo,
  • Li-Ting Huang,
  • Zhiwen Wang

摘要

The algebraic connectivity of a graph is the second smallest eigenvalue of its Laplacian matrix. In this paper, we characterize all the extremal graphs with the maximal algebraic connectivity among all graphs with given order and induced matching number. Furthermore, for trees with given induced matching number, the first three values of the maximal algebraic connectivity and the corresponding extremal trees are also determined.