The skew spectral radius and skew Randić spectral radius of general random oriented graphs

Let G be a simple connected graph on n vertices, and let G sigma be an orientation of G with skew adjacency matrix S(G sigma). Let di be the degree of the vertex vi in G. The skew Randic matrix of G sigma is the n x n real skew symmetric matrix RS(G sigma) = [(RS)ij], where (RS)ij = -(RS)ji = (didj)- 2 if (vi, vj) is 1 an arc of G sigma, and (RS)ij = (RS)ji = 0 otherwise. The skew spectral radius rho S(G sigma) and the skew Randic spectral radius rho RS (G sigma) of G sigma are defined as the spectral radius of S(G sigma) and RS(G sigma) respectively. In this paper we give upper bounds for the skew spectral radius and skew Randic spectral radius of general random oriented graphs. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).