Some inequalities involving the distance signless Laplacian eigenvalues of graphs

Abdollah Alhevaz; Maryam Baghipur; Shariefuddin Pirzada; Yilun Shang

doi:10.22108/toc.2020.121940.1715

Some inequalities involving the distance signless Laplacian eigenvalues of graphs

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

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

35 Downloads (Pure)

Abstract

Given a simple graph G, the distance signless Laplacian D^Q(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 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.

Original language	English
Pages (from-to)	9-29
Number of pages	21
Journal	Transactions on Combinatorics
Volume	10
Issue number	1
DOIs	https://doi.org/10.22108/toc.2020.121940.1715
Publication status	Published - 1 Mar 2021

Keywords

Distance signless Laplacian matrix
eigenvalue
graph operation
spectral radius
transmission regular graph

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TOC_2021 Spring_Vol 10_Issue 1_Pages 9-29Final published version, 313 KBLicence: CC BY

Cite this

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title = "Some inequalities involving the distance signless Laplacian eigenvalues of graphs",

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.",

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author = "Abdollah Alhevaz and Maryam Baghipur and Shariefuddin Pirzada and Yilun Shang",

note = "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.",

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doi = "10.22108/toc.2020.121940.1715",

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AU - Alhevaz, Abdollah

AU - Baghipur, Maryam

AU - Pirzada, Shariefuddin

AU - Shang, Yilun

N1 - 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.

PY - 2021/3/1

Y1 - 2021/3/1

N2 - 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.

AB - 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.

KW - Distance signless Laplacian matrix

KW - eigenvalue

KW - graph operation

KW - spectral radius

KW - transmission regular graph

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JO - Transactions on Combinatorics

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ER -

Some inequalities involving the distance signless Laplacian eigenvalues of graphs

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Keywords

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