On the spectral radius of the generalized adjacency matrix of a digraph

Let D be a strongly connected digraph and alpha is an element of [0, 1]. In Liu et al. (2019) [13] the matrix A(alpha)(D) = alpha Deg(D) +(1-alpha)A(D), where A(D) and Deg(D) are the adjacency matrix and the diagonal matrix of the out-degrees of D, respectively, was de-fined. In this paper it is established some sharp bounds on the A(alpha) (D)-spectral radius in terms of some parameters such as the out-degrees, the maximum out-degree, the second max-imum out-degree, the number of vertices, the number of arcs, the average 2-outdegrees of the vertices of D and the parame-ter alpha of A(alpha) (D). The extremal digraphs attaining these bounds are characterized. It is shown that the bounds obtained im-prove, in some cases, some of recently given bounds presented in the literature. (C) 2022 Elsevier Inc. All rights reserved.