Maximizing the spectral radius of graphs of given size with forbidden a subgraph

Let H₇ denote the 7-vertex fan graph consisting of a 6-vertex path plus a vertex adjacent to each vertex of the path. Let K₃ m-33K₁ be the graph obtained by joining each vertex of a triangle K₃ to m-33 isolated vertices. In this paper, we show that if G is an H₇-free graph with size m 33, then the spectral radius (G) 1+m-2, equality holds if and only if G K₃ m-33K₁ (possibly, with some isolated vertices).