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Some inequalities involving the distance signless Laplacian eigenvalues of graphs | ||
| Transactions on Combinatorics | ||
| دوره 10، شماره 1، خرداد 2021، صفحه 9-29 اصل مقاله (313.37 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.121940.1715 | ||
| نویسندگان | ||
| Abdollah Alhevaz1؛ Maryam Baghipur2؛ Shariefuddin Pirzada3؛ Yilun Shang* 4 | ||
| 1Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box: 316-3619995161, Shahrood, Iran | ||
| 2Department of Mathematics, University of Hormozgan, P. O. Box 3995, Bandar Abbas, Iran | ||
| 3Department of Mathematics, University of Kashmir, Srinagar, India | ||
| 4Department of Computer and Information Sciences, Northumbria University, Newcastle, UK | ||
| چکیده | ||
| Given a simple graph $G$, the distance signlesss Laplacian $D^{Q}(G)=Tr(G)+D(G)$ is the sum of vertex transmissions matrix $Tr(G)$ and distance matrix $D(G)$. In this paper, thanks to the symmetry of $D^{Q}(G)$, we obtain novel sharp bounds on the distance signless Laplacian eigenvalues of $G$, and in particular the distance signless Laplacian spectral radius. The bounds are expressed through graph diameter, vertex covering number, edge covering number, clique number, independence number, domination number as well as extremal transmission degrees. The graphs achieving the corresponding bounds are delineated. In addition, we investigate the distance signless Laplacian spectrum induced by Indu-Bala product, Cartesian product as well as extended double cover graph. | ||
| کلیدواژه‌ها | ||
| Distance signless Laplacian matrix؛ eigenvalue؛ transmission regular graph؛ spectral radius؛ graph operation | ||
| مراجع | ||
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