In this paper we consider the extremal problem on adjacency spectral radius of {C-3, C-5}-free graphs. Assume that G is a graph with m edges having no isolated vertices, and let lambda be the spectral radius of its adjacency matrix. Firstly, by using the method of characterizing {C-3, C-5}-free non-bipartite graphs whose second largest eigenvalue is less than 4 root 5, we show that, if G is a {C-3, C-5}-free non-bipartite graph of size m, then [GRAPHICS] . Equality holds if and only if G congruent to C-7, where d(u) is the degree of vertex u and f denotes the number of 4-cycles in G. Secondly,...
