Question: let g be an undiretced graph with positive weights on...
Let G be an undiretced graph with positive weights on each edges
of the graph. Supposed that a constant a > 0 is added to the
weight of each edge.
(a) Show that the minimum spanning tree does not change.
(b) Give an example to show that the shortest path from some vertex to another vertex may not be the same after adding the constant a.
(c) Give a convincing reason why the two problems behalf differently with respect to adding a constant.