Minimizing the least eigenvalues of unicyclic graphs with application to spectral spread (Q929482)

The spread of a graph is defined to be the difference between the largest eigenvalue and the least eigenvalue of the adjacency matrix of a graph. Let \(\mathcal U_n^k\) denote the set of connected unicyclic graphs of order \(n\) and girth \(k\), and let \(\mathcal U_n\) denote the set of connected unicyclic graphs of order \(n\). It is determined the unique graph with minimum least eigenvalue (respectively, the unique graph with maximum spread) among all graphs in \(\mathcal U_n^k\). In particular, the unique graph with minimum least eigenvalue (respectively, the unique graph with maximum spread) among all graphs in \(\mathcal U_n\) is determined.