Some inequalities involving the distance signless Laplacian eigenvalues of graphs

Alhevaz, Abdollah, Baghipur, Maryam, Pirzada, Shariefuddin and Shang, Yilun (2021) Some inequalities involving the distance signless Laplacian eigenvalues of graphs. Transactions on Combinatorics, 10 (1). pp. 9-29. ISSN 2251-8657

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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.

Item Type: Article
Additional Information: Funding Information: The research of S. Pirzada is supported by DST, New Delhi, and Y. Shang is supported by UoA Flexible Fund No. 201920A1001 from Northumbria University.
Uncontrolled Keywords: Distance signless Laplacian matrix, eigenvalue, graph operation, spectral radius, transmission regular graph
Subjects: G900 Others in Mathematical and Computing Sciences
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: John Coen
Date Deposited: 23 Dec 2021 14:56
Last Modified: 23 Dec 2021 15:00

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