On the maximal α-spectral radius of graphs with given matching number

Abstract

Let be the set of graphs of order n with given matching number β. Let be the diagonal matrix of the degrees of the graph G and be the adjacency matrix of the graph G. The largest eigenvalue of the nonnegative matrix is called the α-spectral radius of G. The graphs with maximal α-spectral radius in are completely characterized in this paper. In this way, we provide a general framework to attack the problem of extremal spectral radius in . More precisely, we generalize the known results on the maximal adjacency spectral radius in and the signless Laplacian spectral radius.