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The \(A_{\alpha}\)-spectral radius of bicyclic graphs with given degree sequences. (English) Zbl 1515.05122

Summary: Let \(A(G)\) and \(D(G)\) be the adjacency matrix and the degree matrix of \(G\), respectively. For any real \(\alpha \in [0,1]\), V. Nikiforov [Appl. Anal. Discrete Math. 11, No. 1, 81–107 (2017; Zbl 1499.05384)] defined the matrix \(A_{\alpha}(G)\) as \[ A_{\alpha} (G) = \alpha D(G) + (1-\alpha) A(G). \] In this paper, we generalize some previous results about the \(A_{1/2}\)-spectral radius of bicyclic graphs with a given degree sequence. Furthermore, we characterize all extremal bicyclic graphs which have the largest \(A_{\alpha}\)-spectral radius in the set of all bicyclic graphs with prescribed degree sequences.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C12 Distance in graphs
05C07 Vertex degrees

Citations:

Zbl 1499.05384
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Full Text: DOI

References:

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