TY - JOUR

T1 - Some inequalities involving the distance signless Laplacian eigenvalues of graphs

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

UR - http://www.scopus.com/inward/record.url?scp=85103125471&partnerID=8YFLogxK

U2 - 10.22108/toc.2020.121940.1715

DO - 10.22108/toc.2020.121940.1715

M3 - Article

AN - SCOPUS:85103125471

SN - 2251-8657

VL - 10

SP - 9

EP - 29

JO - Transactions on Combinatorics

JF - Transactions on Combinatorics

IS - 1

ER -