On Skew Laplacian Spectra and Skew Laplacian Energy of Digraphs

Hilal Ganie, Bilal Chat, S. Pirzada

Let $\mathscr{D}$ be a simple digraph with $n$ vertices, $m$ arcs having skew Laplacian eigenvalues $\nu_1, \nu_2, …, \nu_{n-1},\nu_n=0$. The skew Laplacian energy $SLE(\mathscr{D})$ of a digraph $\mathscr{D}$ is defined as $SLE(\mathscr{D})=\sum_{i=1}^{n}|\nu_i|$. We obtain upper and lower bounds for $SLE(\mathscr{D})$, which improves some previously known bounds. We also show that every even positive integer is indeed the skew Laplacian energy of some digraph.