On the A_α-spectral radius of graphs without linear forests

2023/04/06 by Chen, Ming-Zhu, Liu, A-Ming, Zhang, Xiao-Dong · 2 citations
#05C35 #05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.03046

Abstract

Let A(G) and D(G) be the adjacency and degree matrices of a simple graph G on n vertices, respectively. The A_α-spectral radius of G is the largest eigenvalue of A_α(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 A_α-spectral radius of graphs on n vertices without a subgraph isomorphic to a liner forest for n large enough and characterize all graphs which attain the upper bound. As a result, we completely obtain the maximum signless Laplacian spectral radius of graphs on n vertices without a subgraph isomorphic to a liner forest for n large enough.

Cited by

• The α-spectral Turán type problems for graphs
• Extremal graphs for the maximum A_α-spectral radius of graphs with order and size

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