Some Spectral Inequalities for Triangle-Free Regular Graphs

Tamara Koledin, Zoran Stanić

We give three general bounds on the diameter, degree and order of triangle-free regular graphs with bounded second largest eigenvalue. Next, we consider bipartite regular graphs and present another four inequalities that bound the order of such graphs in terms of their degree and their second largest eigenvalue. We also prove some consequences and indicate graphs for which the corresponding bounds are attained.