Some inequalities involving the distance signless Laplacian eigenvalues of graphs
نویسندگان
1 Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box: 316-3619995161, Shahrood, Iran
2 Department of Mathematics, University of Kashmir, Srinagar, India.
3 Department of Mathematics, University of Hormozgan, P. O. Box 3995, Bandar Abbas, Iran
4 Department of Computer and Information Sciences, Northumbria University, Newcastle, UK
doi
10.22108/toc.2020.121940.1715چکیده
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.
