NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS

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.

Keywords:

‎Distance signless Laplacian matrix , spectral radius , extremal graph , transmission regular graph