Spectral Radius of Graphs with Given Diameter

Abstract

In this paper, we show that among all connected graphs of order $n$ with diameter $D$, the graph $G^{\ast }$ has maximal spectral radius, where $G^{\ast }$ is obtained from $K_{n-D}\bigvee \overline{K_2}$ by attaching two paths of order $l_1$ and $l_2$ to the two vertices $u,v$ in $\overline{K_2}$, respectively, and $l_1+l_2=D-2$, $|l_1–l_2|\le 1$.