(a) prove that every graph of order $\displaystyle n \geq 4$ and size $\displaystyle n + 1$ contains $\displaystyle K_{1,3}$ as a subgraph

(b) describe the graphs of order $\displaystyle n \geq 4$ and size $\displaystyle n$ that do not contain $\displaystyle K_{1,3}$ as a subgraph