A path of order $n$ is denoted by $P_n$, and a star of order $n$ is denoted by $S_{ n-1}$. A star-path forest is a forest whose connected components are paths and stars. In this paper we determine the maximum spectral radius of graphs that contain no copy of $kS_{ \ell-1}\cup P_{ \ell}$, $k_1S_{ 2\ell -1}\cup k_2P_{ 2\ell}$ or $kS_{ 4}\cup 2P_{ 5}$ for $n$ appropriately large.
Categories: math.CO