1
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Which of the following statements is/are TRUE for a group G?

A
If for all x, y $$\in$$ G, (xy)2 = x2y2, then G is commutative.
B
If for all X $$\in$$ G, x2 = 1, then G is commutative. Here, 1 is the identity element of G.
C
If the order of G is 2, then G is commutative.
D
If G is commutative, then a subgroup of G need not be commutative.
2
GATE CSE 2022
Numerical
+1
-0.33

Consider a simple undirected graph of 10 vertices. If the graph is disconnected, then the maximum number of edges it can have is __________.

Your input ____
3
GATE CSE 2022
MCQ (Single Correct Answer)
+1
-0.33

Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trace of

A
A3
B
A3 divided by 2
C
A3 divided by 3
D
A3 divided by 6
4
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of G is/are TRUE?

A
The edge with the second smallest weight is always part of any minimum spanning tree of G.
B
One or both of the edges with the third smallest and the fourth smallest weights are part of any minimum spanning tree of G.
C
Suppose S $$\subseteq$$ V be such that S $$\ne$$ $$\phi$$ and S $$\ne$$ V. Consider the edge with the minimum weight such that one of its vertices is in S and the other in V \ S. Such an edge will always be part of any minimum spanning tree of G.
D
G can have multiple minimum spanning trees.
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