%0 Journal Article
%T More on the bounds for the skew Laplacian energy of weighted digraphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Chat, Bilal Ahmad
%A Samee, Uma Tul
%A Pirzada, Shariefuddin
%D 2023
%\ 06/01/2023
%V 8
%N 2
%P 379-390
%! More on the bounds for the skew Laplacian energy of weighted digraphs
%K Weighted digraph
%K skew Laplacian matrix of weighted digraphs
%K skew Laplacian energy of weighted digraphs
%R 10.22049/cco.2022.27357.1244
%X Let $mathscr{D}$ be a simple connected digraph with $n$ vertices and $m$ arcs and let $W(mathscr{D})=mathscr{D},w)$ be the weighted digraph corresponding to $mathscr{D}$, where the weights are taken from the set of non-zero real numbers. Let $nu_1,nu_2, dots,nu_n$ be the eigenvalues of the skew Laplacian weighted matrix $widetilde{SL}W(mathscr{D})$ of the weighted digraph $W(mathscr{D})$. In this paper, we discuss the skew Laplacian energy $widetilde{SLE}W(mathscr{D})$ of weighted digraphs and obtain the skew Laplacian energy of the weighted star $W(mathscr{K}_{1, n})$ for some fixed orientation to the weighted arcs. We obtain lower and upper bounds for $widetilde{SLE}W(mathscr{D})$ and show the existence of weighted digraphs attaining these bounds.
%U http://comb-opt.azaruniv.ac.ir/article_14373_7516a2473863a0383b257ba88adfeb19.pdf