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 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 . 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 . 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