Spectral extrema of graphs with fixed size: cycles and complete bipartite graphs

Mingqing Zhai, Huiqiu Lin, Jinlong Shu

Nikiforov [Some inequalities for the largest eigenvalue of a graph, Combin. Probab. Comput. 179--189] showed that if $G$ is $K_{r+1}$-free then the spectral radius $ρ(G)\leq\sqrt{2…