TY - JOUR
ID - 14373
TI - More on the bounds for the skew Laplacian energy of weighted digraphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Chat, Bilal Ahmad
AU - Samee, Uma Tul
AU - Pirzada, Shariefuddin
AD - Department of Mathematical Sciences
IUST Awantipora Pulwama Jammu and Kashmir India
AD - Institute of Technology
University of Kashmir
AD - Department of Mathematics, Hazratbal
Y1 - 2023
PY - 2023
VL - 8
IS - 2
SP - 379
EP - 390
KW - Weighted digraph
KW - skew Laplacian matrix of weighted digraphs
KW - skew Laplacian energy of weighted digraphs
DO - 10.22049/cco.2022.27357.1244
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_14373.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14373_7516a2473863a0383b257ba88adfeb19.pdf
ER -