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

Abstract

Let G be a simple connected graph on n vertices, and let Gσ be an orientation of G with skew adjacency matrix S(Gσ). Let di be the degree of the vertex vi in G. The skew Randić matrix of Gσ is the n×n real skew symmetric matrix RS(Gσ)=[(RS)ij], where (RS)ij=−(RS)ji=(didj)−12 if (vi,vj) is an arc of Gσ, and (RS)ij=(RS)ji=0 otherwise. The skew spectral radius ρS(Gσ) and the skew Randić spectral radius ρRS(Gσ) of Gσ are defined as the spectral radius of S(Gσ) and RS(Gσ) respectively. In this paper we give upper bounds for the skew spectral radius and skew Randić spectral radius of general random oriented graphs.