Minimizing the least eigenvalues of unicyclic graphs with application to spectral spread Original Research Article

The spread of a graph is defined to be the difference between the largest eigenvalue and the least eigenvalue of the adjacency matrix of the graph. Let image denote the set of connected unicyclic graphs of order n and girth k, and let image denote the set of connected unicyclic graphs of order n. In this paper, we determine the unique graph with minimum least eigenvalue (respectively, the unique graph with maximum spread) among all graphs in image. We, finally, characterize the unique graph with minimum least eigenvalue (respectively, the unique graph with maximum spread) among all graphs in image.