2018/06/07 by Dan Li, Yuanyuan Chen, Li, Dan +3
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1806.02603
openalex publication_date 2018/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a graph with adjacency matrix A(G), and let D(G) be the\ndiagonal matrix of the degrees of G. For any real \α\∈[0,1], write\nA_\α(G) for the matrix A_
alpha(G)=
alpha D(G)+(1-
alpha)A(G). This\npaper presents some extremal results about the spectral radius\n\ρ(A_\α(G)) of A_\α(G) that generalize previous results about\n\ρ(A0(G)) and \ρ(A\(1)/(2)(G)). In this paper, we give some\nresults on graph perturbation for A_\α-matrix with \α\∈ [0,1). As\napplications, we characterize all extremal trees with the maximum\nA_\α-spectral radius in the set of all trees with prescribed degree\nsequence firstly. Furthermore, we characterize the unicyclic graphs that have\nthe largest A_\α-spectral radius for a given unicycilc degree sequence.\n