On the Spectra of Tricyclic Graphs

Abstract

Let \(\mathcal{J}_n\) be the set of tricyclic graphs of order \(n\). In this paper, we use a new proof to determine the unique graph with maximal spectral radius among all graphs in \(\mathcal{J}_n\) for each \(n \geq 4\). Also, we determine the unique graph with minimal least eigenvalue among all graphs in this class for each \(n \geq 52\). We can observe that the graph with maximal spectral radius is not the same as the one with minimal least eigenvalue in \(\mathcal{J}_n\), which is different from those on the unicyclic and bicyclic graphs.