On the Aα-spectral radius of graphs without linear forests

Ming-Zhu Chen, A-Ming Liu and Xiao-Dong Zhang

Applied Mathematics and Computation, 2023, vol. 450, issue C

Abstract: Let A(G) and D(G) be the adjacency and degree matrices of a simple graph G on n vertices, respectively. The Aα-spectral radius of G is the largest eigenvalue of Aα(G)=αD(G)+(1−α)A(G) for a real number α∈[0,1]. In this paper, for α∈(0,1), we obtain a sharp upper bound for the Aα-spectral radius of graphs on n vertices without a subgraph isomorphic to a linear forest for n large enough and characterize all graphs which attain the upper bound. As a result, we completely dertermine the maximum signless Laplacian spectral radius of graphs on n vertices without a subgraph isomorphic to a linear forest for n large enough.

Keywords: Aα-spectral radius; Extremal graphs; Linear forests (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001741

DOI: 10.1016/j.amc.2023.128005

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