GATE CSE 2021 Set 1 | Graph Theory Question 15 | Discrete Mathematics

GATE CSE 2021 Set 1

MCQ (More than One Correct Answer)

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An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components.

Let T be a DFS tree obtained by doing DFS in a connected undirected graph G. Which of the following option is/are correct?

If u is an articulation point in G such that x is an ancestor of u in T and y is a descendent of u in T, then all paths from x to y in G must pass through u.

Root of T is an articulation point in G if and only if it has 2 or more children.

Root of T can never be an articulation point in G.

A leaf of T can be an articulation point in G.

GATE CSE 2021 Set 1

MCQ (Single Correct Answer)

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Let G be a group order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?

G is always cyclic, but H may not be cyclic.

G may not be cyclic, but H is always cyclic.

Both G and H are always cyclic.

Both G and H may not be cyclic.

GATE CSE 2021 Set 1

Numerical

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In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is ______

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GATE CSE 2020

Numerical

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Graph G is obtained by adding vertex s to K_3,4 and making s adjacent to every vertex of K_3,4. The minimum number of colours required to edge-colour G is _____.

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