Extremal graphs for disjoint union of stars and paths

Let $F$ be a graph. A graph $G$ is called $F$-free if $G$ does not contain $F$ as a subgraph. Let $\mathrm{E}\mathrm{X}(n,F)$ denote the set of $F$-free graphs of order $n$ with the maximum edges. In this paper, we characterize the graphs in $\mathrm{E}\mathrm{X}(n,F)$ for large $n$, where $F$ is the disjoint union of paths and stars. This generalizes a result in \cite{LLP}.