GATE CSE 2022 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2022

MCQ (More than One Correct Answer)

-0.67

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?

The edge with the second smallest weight is always part of any minimum spanning tree of G.

One or both of the edges with the third smallest and the fourth smallest weights are part of any minimum spanning tree of G.

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.

G can have multiple minimum spanning trees.

GATE CSE 2022

MCQ (More than One Correct Answer)

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The following simple undirected graph is referred to as the Peterson graph.

GATE CSE 2022 Discrete Mathematics - Graph Theory Question 13 English

Which of the following statements is/are TRUE?

The chromatic number of the graph is 3.

The graph has a Hamiltonian path.

The following graph is isomorphic to the Peterson graph.

GATE CSE 2022 Discrete Mathematics - Graph Theory Question 13 English Option 3

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.)

GATE CSE 2022

MCQ (Single Correct Answer)

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

The diagonal entries of A² are the degrees of the vertices of the graph.

If the graph is connected, then none of the entries of A^{n $$-$$ 1} + I_n can be zero.

If the sum of all the elements of A is at most 2(n $$-$$ 1), then the graph must be acyclic.

If there is at least a 1 in each of A's rows and columns, then the graph must be connected.

GATE CSE 2022

MCQ (More than One Correct Answer)

-0.67

Which of the following is/are the eigenvector(s) for the matrix given below?

$$\left( {\matrix{ { - 9} & { - 6} & { - 2} & { - 4} \cr { - 8} & { - 6} & { - 3} & { - 1} \cr {20} & {15} & 8 & 5 \cr {32} & {21} & 7 & {12} \cr } } \right)$$

$$\left( {\matrix{ { - 1} \cr 1 \cr 0 \cr 1 \cr } } \right)$$

$$\left( {\matrix{ 1 \cr 0 \cr { - 1} \cr 0 \cr } } \right)$$

$$\left( {\matrix{ { - 1} \cr 0 \cr 2 \cr 2 \cr } } \right)$$

$$\left( {\matrix{ 0 \cr 1 \cr { - 3} \cr 0 \cr } } \right)$$

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