@article {
author = {Chat, Bilal and Samee, Uma Tul and Pirzada, Shariefuddin},
title = {More on the bounds for the skew Laplacian energy of weighted digraphs},
journal = {Communications in Combinatorics and Optimization},
volume = {8},
number = {2},
pages = {379-390},
year = {2023},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2022.27357.1244},
abstract = {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. },
keywords = {Weighted digraph,skew Laplacian matrix of weighted digraphs,skew Laplacian energy of weighted digraphs},
url = {http://comb-opt.azaruniv.ac.ir/article_14373.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14373_7516a2473863a0383b257ba88adfeb19.pdf}
}