The Aα-spectral radius of trees and unicyclic graphs with given degree sequence

摘要

For any real α ∈ [0, 1], Aα(G)=αD(G)+(1−α)A(G) is the Aα-matrix of a graph G, where A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the degrees of G. This paper presents some extremal results about the spectral radius λ1(Aα(G)) of Aα(G) that generalize previous results about λ1(A0(G)) and λ1(A12(G)). In this paper, we study the behavior of the Aα-spectral radius under some graph transformations for α ∈ [0, 1). As applications, we show that the greedy tree has the maximum Aα-spectral radius in GD when D is a tree degree sequence firstly. Furthermore, we determine that the greedy unicyclic graph has the largest Aα-spectral radius in GD when D is a unicyclic graphic sequence, where GD={G∣GisconnectedwithDasitsdegreesequence}.