On the Largest Eigenvalue of Unicyclic Graphs

Slobodan_K. Simić

We first establish some relations between the graph structure and its largest eigenvalue. Applying these results to unicyclic graphs (with a fixed number of points), we explain some facts about the $\lambda_1$-ordering of these graphs. Most of these facts were suggested by the experiments conducted on the expert system "GRAPH", which has been developed and implemented at the Faculty of Electrical Engineering, University of Belgrade.