The spectral Turan problem about graphs of given size with forbidden subgraphs

Let G be a graph of size m and rho(G) be the spectral radius of its adjacency matrix. A graph is said to be H-free if it does not contain a subgraph isomorphic to H. Let C-l(1) be the graph obtained by adding a pendent vertex to a cycle of length l. In this paper, we determine the graphs with the maximum spectral radius over C-3(1) -free graphs, and C-4(1) -free graphs with m >= 9 .