The Aα-spectral radius of graphs with a prescribed number of edges for 1/2 ≤ α ≤ 1

For 0 <= alpha <= 1, the A(alpha)-matrix of graph G is defined as A(alpha)(G) = alpha D(G) + (1 - alpha)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(alpha)-spectral radius for alpha is an element of [1/2, 1]. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper extends the study on maximizing the spectral radius under a fixed number of edges, concerning the A(alpha)-matrix.