On the Distance Signless Laplacian Spectral Radius of Bicyclic Graphs

Abstract:

      The distance signless Laplacian matrix of a connected graph $G$ is defined as $\mathcal{Q}(G)=Tr(G)+D(G)$, where $Tr(G)$ is the diagonal matrix of the vertex transmissions in $G$ and $D(G)$ is the distance matrix of $G$. The largest eigenvalue of the distance signless Laplacian matrix is called the distance signless Laplacian spectral radius of $G$. In this paper, we determine the unique graph with the maximum distance signless Laplacian spectral radius among all the bicyclic graphs with given order.