In a connected graph, the distance d(v,w) between vertex v and vertex w is the length of the shortest edges from v to w.

a) if d(v,w)≥2 show that there exists a vertex z such that, d(v,z)+d(z,w)=d(v,w)

b) in the petersen graph show that d(v,w)=1 or 2, for any distinct vertices v and w