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More on the bounds for the skew Laplacian energy of weighted digraphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 7، دوره 8، شماره 2، شهریور 2023، صفحه 379-390 اصل مقاله (421.91 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27357.1244 | ||
| نویسندگان | ||
| Bilal Ahmad Chat1؛ Uma Tul Samee2؛ Shariefuddin Pirzada* 3 | ||
| 1Department of Mathematical Sciences IUST Awantipora Pulwama Jammu and Kashmir India | ||
| 2Institute of Technology University of Kashmir | ||
| 3Department of Mathematics, Hazratbal | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Weighted digraph؛ skew Laplacian matrix of weighted digraphs؛ skew Laplacian energy of weighted digraphs | ||
| مراجع | ||
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