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 \(G^*\) has maximal spectral radius, where \(G^*\) 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 \(l_1 + l_2 = D-2\), \(|l_1 – l_2| \leq 1\).