Bounds for the skew Laplacian (skew adjacency) spectral radius of a digraph

Abstract

‎‎For a simple connected graph $G$ with $n$ vertices and $m$ edges‎, ‎let $overrightarrow{G}$ be a digraph obtained by giving an arbitrary direction to the edges of $G$‎. ‎In this paper‎, ‎we consider the skew Laplacian/skew adjacency matrix of the digraph $overrightarrow{G}$‎. ‎We obtain upper bounds for the skew Laplacian/skew adjacency spectral radius‎, ‎in terms of various parameters (like oriented degree‎, ‎average oriented degree) associated with the structure of the digraph $overrightarrow{G}$‎. ‎We also obtain upper and lower bounds for the skew Laplacian/skew adjacency spectral radius‎, ‎in terms of skew Laplacian/skew adjacency rank of the digraph $overrightarrow{G}$‎.