Document Type : Original Manuscript


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.


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 $D^{Q}(G)=Tr(G)+D(G)$, where $D(G)$ is the distance matrix of $G$ and $Tr(G)$ 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.