Skip to content
Related Articles

Related Articles

Improve Article

GATE | GATE-CS-2000 | Question 41

  • Last Updated : 28 Jun, 2021
Geek Week

Let G be an undirected connected graph with distinct edge weight. Let emax be the edge with maximum weight and emin the edge with minimum weight. Which of the following statements is false?
(A) Every minimum spanning tree of G must contain emin
(B) If emax is in a minimum spanning tree, then its removal must disconnect G
(C) No minimum spanning tree contains emax
(D) G has a unique minimum spanning tree

Answer: (C)


In kruskal’s algorithm, we pick the edges in ascending order and add them to the forest if no cycle is formed. Option A is True because first edge could never create a cycle.
The only reason for emax to be present in the minimum spanning tree could be that it is the only possible edge to cover a particular vertex in a tree since all vertices have to be present in a spanning tree by definition. Consider the image below


See question 2 of

This solution is contributed by Pranjul Ahuja

Quiz of this Question

Attention reader! Don’t stop learning now.  Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.

Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up
Recommended Articles
Page :