1
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.
2
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are TRUE?

A
The chromatic number of the graph is 3.
B
The graph has a Hamiltonian path.
C

The following graph is isomorphic to the Peterson graph. D
The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
3
GATE CSE 2022
+1
-0.33

Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?

A
The diagonal entries of A2 are the degrees of the vertices of the graph.
B
If the graph is connected, then none of the entries of An $$-$$ 1 + In can be zero.
C
If the sum of all the elements of A is at most 2(n $$-$$ 1), then the graph must be acyclic.
D
If there is at least a 1 in each of A's rows and columns, then the graph must be connected.
4
GATE CSE 2021 Set 2
+1
-0.33

Let G be a connected undirected weighted graph. Consider the following two statements.

S1: There exists a minimum weight edge in G which is present in every minimum spanning tree of G.

S2: If every edge in G has distinct weight, then G has a unique minimum spanning tree. Which one of the following options is correct?

A
S1 is false and S2 is true.
B
S1 is true and S2 is false.
C
Both S1 and S2 are true.
D
Both S1 and S2 are false.
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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