Which of the following option is incorrect regarding minimum spanning tree?
(A) In an adjacency matrix for an undirected graph with 5 nodes. If all diagonal element is 0 and all non-diagonal element is 1 then there will be multiple distinct MST of cost 4.
(B) In an undirected graph G with distinct edge weight if e_max is the edge with maximum weight and e_min is the edge with minimum weight then no minimum spanning tree contain e_max.
(C) In an undirected graph G with distinct edge weight if e_max is the edge with maximum weight and e_min is the edge with minimum weight. If e_max is in a minimum spanning tree, then its removal must disconnect G.
(D) In a weighted undirected graph with distinct edges, if every edge weight is increased by same weight then minimum spanning tree does not changed.


Answer: (B)

Explanation: In an undirected graph G with distinct edge weight if e_max is the edge with maximum weight and e_min is the edge with minimum weight then G has unique minimum spanning tree, If e_max is in a minimum spanning tree, then its removal must disconnect G, every minimum spanning tree of G must contain e_min but its not necessary that no minimum spanning tree contains e_max.
So, option (B) is correct.

Quiz of this Question