Title of article :
Some inequalities involving the distance signless Laplacian eigenvalues of graphs
Author/Authors :
Alhevaz, Abdollah Faculty of Mathematical Sciences - Shahrood University of Technology, hahrood, Iran , Baghipur, Maryam Department of Mathematics - University of Hormozgan, Bandar Abbas, Iran , Pirzada, Shariefuddin Department of Mathematics - University of Kashmir, Srinagar, India , Shang, Yilun Department of Computer and Information Sciences - Northumbria University, Newcastle, UK
Abstract :
Given a simple graph G, the distance signlesss Laplacian DQ(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 DQ(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.
Keywords :
Distance signless , Laplacian matrix , eigenvalue , transmission regular graph , spectral radius , graph operation
Journal title :
Transactions on Combinatorics
