GATE 2005
March 12, 2025GATE 2005
March 12, 2025GATE 2005
| Question 6 |
An undirected graph C has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0’s and (ii) non-diagonal elements are l’s. Which one of the following is TRUE?
| Graph G has no minimum spanning tree (MST)
| |
| Graph G has a unique MST of cost n-1 | |
| Graph G has multiple distinct MSTs, each of cost n-1 | |
| Graph G has multiple spanning trees of different costs |
Question 6 Explanation:
From given data, we can say that the given graph is complete graph with all edge weights 1. Hence weight of MST is n-1.
Since the weights of every edge is 1 so there are different MST’s are possible with same cost, i.e., (n-1).
Since the weights of every edge is 1 so there are different MST’s are possible with same cost, i.e., (n-1).
Correct Answer: C
Question 6 Explanation:
From given data, we can say that the given graph is complete graph with all edge weights 1. Hence weight of MST is n-1.
Since the weights of every edge is 1 so there are different MST’s are possible with same cost, i.e., (n-1).
Since the weights of every edge is 1 so there are different MST’s are possible with same cost, i.e., (n-1).