Practice Question 5 - 4.6 | 4. Prof. Ashish Choudhury | Discrete Mathematics - Vol 3
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4.6 - Question 5

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the vertex chromatic number?

💡 Hint: Think of a scenario where you need to color a map.

Question 2

Easy

Consider two graphs F and H with chromatic numbers of 3 and 4, respectively. What can you conclude about the chromatic number of their union graph G?

💡 Hint: Reflect on the concepts of overlapping colors when vertices are united.

Practice 1 more question and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the vertex chromatic number of a complete graph with 5 vertices?

  • 1
  • 2
  • 5
  • 3

💡 Hint: Consider the total number of vertices.

Question 2

True or False: The chromatic number of the union of two graphs is always equal to the sum of their individual chromatic numbers.

  • True
  • False

💡 Hint: Think about how colors might overlap.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given two graphs, one with a chromatic number of 2 and another with a chromatic number of 5, explore the possible chromatic numbers of their union and explain your reasoning.

💡 Hint: Reflect upon overlapping edges and colors as members join.

Question 2

Create a complete bipartite graph and a disconnected graph, calculate their chromatic numbers, and analyze their union chromatic number.

💡 Hint: Visualize both graphs and imagine their union.

Challenge and get performance evaluation