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 -