Clique Number and Distance Spectral Radii of Graphs

Abstract

The distance spectral radius of a connected graph $G$, denoted by $\rho (G)$, is the maximal eigenvalue of the distance matrix of $G$. In this paper, we find a sharp lower bound as well as a sharp upper bound of $\rho (G)$ in terms of $\omega (G)$, the clique number of $G$. Furthermore, both extremal graphs are uniquely determined.