new skew laplacian energy of simple digraphs

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g)=d^+(g)-d^-(g)$ and$s(g)$ is the skew-adjacency matrix of $g$, and from which we definethe skew laplacian energy $sle(g)$ of $g$ as the sum of the norms ofall the eigenvalues of $widetilde{sl}(g)$. some lower and upperbounds of the new skew laplacian energy are derived and the digraphsattaining these bounds are also determined.