For every undirected unweighted graph is every MST also a SPT
Counter example: V={a,b,c,d}, E={(a,b), (a,c), (a,d), (b,c)}.
A MST of this graph, rooted at a, could be: {(a,b), (a,d), (b,c)}. But this is not a SPT because the path a-&gt;c is of length 2 instead of 1 (a and c are directly connected in the original graph).