1
GATE CSE 2021 Set 1
MCQ (More than One Correct Answer)
+2
-0.67

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?

A
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.
B
Root of T is an articulation point in G if and only if it has 2 or more children.
C
Root of T can never be an articulation point in G.
D
A leaf of T can be an articulation point in G.
2
GATE CSE 2021 Set 1
+2
-0.67
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?
A
G is always cyclic, but H may not be cyclic.
B
G may not be cyclic, but H is always cyclic.
C
Both G and H are always cyclic.
D
Both G and H may not be cyclic.
3
GATE CSE 2021 Set 1
Numerical
+2
-0.67
In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is ______
4
GATE CSE 2020
Numerical
+2
-0.67
Graph G is obtained by adding vertex s to K3,4 and making s adjacent to every vertex of K3,4. The minimum number of colours required to edge-colour G is _____.