On the maximal α-spectral radius of graphs with given matching number,Linear and Multilinear Algebra

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On the maximal α-spectral radius of graphs with given matching number
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2022-05-04 , DOI: 10.1080/03081087.2022.2071412
Xiying Yuan ₁ , Zhenan Shao ₁

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Let $G_{n, β}$ be the set of graphs of order n with given matching number β. Let $D (G)$ be the diagonal matrix of the degrees of the graph G and $A (G)$ be the adjacency matrix of the graph G. The largest eigenvalue of the nonnegative matrix $A_{α} (G) = α D (G) + A (G)$ is called the α-spectral radius of G. The graphs with maximal α-spectral radius in $G_{n, β}$ are completely characterized in this paper. In this way, we provide a general framework to attack the problem of extremal spectral radius in $G_{n, β}$ . More precisely, we generalize the known results on the maximal adjacency spectral radius in $G_{n, β}$ and the signless Laplacian spectral radius.

更新日期：2022-05-04

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