The A-spectral radius of graphs with a prescribed number of edges for 12≤α≤1

For 0 ≤ α ≤ 1 , the A α -matrix of graph G is defined as A α ( G ) = α D ( G ) + ( 1 − α ) A ( G ) , where D ( G ) and A ( G ) are the diagonal matrix of the degrees and the adjacency matrix of G, respectively. On the premise of a fixed number of edges, Zhai et al. (2020) [15] depicted the extremal graph which has the largest A 1 2 -spectral radius, and also characterized the graph maximizing the A 1 2 -spectral radius among all graphs with given clique number (respectively, chromatic number). In this paper, we extend the conclusion of them to A α -spectral radius for α ∈ [ 1 2 , 1 ] .