On the Spectral Radius of Unicyclic Graphs with Fixed Girth

Abstract

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Let \(\mathcal{G}\) be the set of unicyclic graphs of order \(n\) with girth \(g\). For all integers \(n\) and \(g\) with \(5 \leq g \leq n – 6\), we determine the first \(|\frac{g}{2}| + 3\) spectral radii of unicyclic graphs in the set \(\mathcal{U}_n^g\).