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1
GATE CSE 2026 Set 1
Numerical
+2
-0

Let $G$ be an undirected graph, which is a path on 8 vertices. The number of matchings in $G$ is $\_\_\_\_$ (answer in integer)

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2
GATE CSE 2024 Set 2
Numerical
+2
-0

The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. The chromatic number of the following graph is ________

GATE CSE 2024 Set 2 Discrete Mathematics - Graph Theory Question 5 English

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3
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+2
-0

The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic number $k$. Which of the following statements is/are always TRUE?

A

$G$ contains a complete subgraph with $k$ vertices

B

$G$ contains an independent set of size at least $n/k$

C

$G$ contains at least $k(k-1)/2$ edges

D

$G$ contains a vertex of degree at least $k$

4
GATE CSE 2024 Set 1
Numerical
+2
-0

The number of edges present in the forest generated by the DFS traversal of an undirected graph G with 100 vertices is 40. The number of connected components in G is ________

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