Help with definition on regular graph

Question

What does it mean $\frac{n-1}{2}K_{2}$? In general which graph am I referring to if I write $l\times K_{2}$? To add a little bit of contest, we are talking about undirected graph on n-1 vertices with adjacency matrix A, Denote the eigenvalues of A by $\lambda_{1}\geq \lambda_{2}\geq…\geq\lambda_{n-1}$. Then “it is well-known” that $\lambda_{2}\leq-1$ if and only if $\mathcal{G}=K_{n-1}$ and $\lambda_{n-1}\geq-1 $ if and only if $\mathcal{G}=\frac{n-1}{2}K_{2}$, where $\mathcal{G}$ is the graph associated to that adjacency matrix A.