Some inequalities involving the distance signless Laplacian eigenvalues of graphs

Abdollah Alhevaz, Maryam Baghipur, Shariefuddin Pirzada, Yilun Shang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

Given a simple graph G, the distance signless Laplacian DQ(G) = Tr(G) + D(G) is the sum of vertex transmissions matrix T r(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.

Original languageEnglish
Pages (from-to)9-29
Number of pages21
JournalTransactions on Combinatorics
Volume10
Issue number1
DOIs
Publication statusPublished - 1 Mar 2021

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