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 $5\le g\le n–6$, we determine the first $|\frac{g}{2}|+3$ spectral radii of unicyclic graphs in the set ${\mathcal{U}}_n^g$.