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 $overrightarrow{G}$.
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