Decorations

The controls team has come up with an idea of decorating BITS Goa on the occasion of Quark. The lighting can be considered as a connected graph G. All the edges initially are in the off state. The control team can choose vertex $u,v$. All the edges in the shortest path between $u$ and $v$ are toggled. If there are more than one sequence of shortest paths than the lexicographically smallest is cho