On the spectral radius of graphs without a gem

The gem is the 5-vertex graph consisting of a 4-vertex path plus a vertex adjacent to each vertex of the path. A graph is said to be gem-free if it does not contain gem as a subgraph. In this paper, we consider the spectral extremal problem for gem-free graphs with given size. The maximum spectral radius of gem-free graphs with size m≥11 is obtained, and the unique corresponding extremal graph is determined.