The $A_{\alpha}$-spectral Radius of Bicyclic Graphs with Given Degree Sequences

Abstract

Let A(G) and D(G) be the adjacency matrix and the degree matrix of G, respectively. For any real α ∈ [0, 1], Nikiforov defined the matrix A α (G) asIn 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 α -spectral radius in the set of all bicyclic graphs with prescribed degree sequences.