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      The \(A_\alpha\)-spectral radius of graphs with given degree sequence

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          Abstract

          Let \(G\) be a graph with adjacency matrix \(A(G)\), and let \(D(G)\) be the diagonal matrix of the degrees of \(G\). For any real \(\alpha\in[0,1]\), write \(A_\alpha(G)\) for the matrix \[A_\alpha(G)=\alpha D(G)+(1-\alpha)A(G).\] This paper presents some extremal results about the spectral radius \(\rho(A_\alpha(G))\) of \(A_\alpha(G)\) that generalize previous results about \(\rho(A_0(G))\) and \(\rho(A_{\frac{1}{2}}(G))\). In this paper, we give some results on graph perturbation for \(A_\alpha\)-matrix with \(\alpha\in [0,1)\). As applications, we characterize all extremal trees with the maximum \(A_\alpha\)-spectral radius in the set of all trees with prescribed degree sequence firstly. Furthermore, we characterize the unicyclic graphs that have the largest \(A_\alpha\)-spectral radius for a given unicycilc degree sequence.

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          On the Aα-spectra of trees

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            The Laplacian spectral radii of trees with degree sequences

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              Merging the A-and Q-spectral theories

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                Author and article information

                Journal
                07 June 2018
                Article
                1806.02603
                34f7f52e-f1f4-4846-bf56-49fea2d9de4f

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.CO

                Combinatorics
                Combinatorics

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