Let (eccentricity of v)$\displaystyle e(v)=Max_{u \in V(G)} d(u,v)$ and $\displaystyle diam(G)= Max_{v \in V(G)} e(v)$, where V(G) is the set of vertices of G and d(u,v) is the distance between u and v. Let (periphery of G) Pe(G) be the graph induced by the vertices of G that have eccentricity equivalent to diam(G). Now suppose that the graph H has n vertices. Prove that H is Pe(G) if and only if $\displaystyle \Delta(H) \le n-2$. ($\displaystyle \Delta(H)$ is the maximum degree in H)