BOUNDS FOR THE SKEW LAPLACIAN (SKEW ADJACENCY) SPECTRAL RADIUS OF A DIGRAPH

For a simple connected graph G with n vertices and m edges, let (G) over right arrow 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 (G) over right arrow. 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 (G) over right arrow. 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 (G) over right arrow.