UGC NET CSE | November 2017 | Part 2 | Question: 23

Question

Let $G$ be an undirected connected graph with distinct edge weight. Let $E_{\text{max}}$ be the edge with maximum weight and $E_{\text{min}}$ the edge with minimum weight. Which of the following statements is false?

• A. Every minimum spanning tree of $G$ must contain $E_{\text{min}}$
• B. If $E_{\text{max}}$ is in minimum spanning tree, then its removal must disconnect $G$
• C. No minimum spanning tree contains $E_{\text{max}}$
• D. $G$ has a unique minimum spanning tree

Comments

Option C is correct.

Answer 1

Option 3 is false. There may exist some spanning trees which consist of emax in it and its removal must disconnect the graph G.