NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS

Document Type : Original Manuscript

Authors

¹ Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box: 316-3619995161, Shahrood, Iran.

² Department of Mathematics, University of Hormozgan, P.O. Box 3995, Bandar Abbas, Iran.

³ Department of Applied Sciences, Tezpur University, Tezpur-784028, India.

Abstract

The distance signless Laplacian spectral radius of a connected graph

G

is the largest eigenvalue of the distance signless Laplacian matrix of

G

, defined as

D^{Q} (G) = T r (G) + D (G)

, where

D (G)

is the distance matrix of

G

and

T r (G)

is the diagonal matrix of vertex transmissions of

G

. In this paper, we determine some new upper and lower bounds on the distance signless Laplacian spectral radius of

G

and characterize the extremal graphs attaining these bounds.

Keywords

20.1001.1.23455128.2021.8.2.8.3