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Chapter 10: Q9E (page 733)

Find the chromatic number of the given graph.

Short Answer

Expert verified

The Chromatic number of the given graph is \(2\).

Step by step solution

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01

Given data in the question.

In the question, a graph is given.

02

Definition to be used.

According to the definition of chromatic number of a graph, the chromatic number of a graph is the least number of colors needed to color a graph so that no two adjacent vertices are assigned the same color.

03

Find the chromatic number of the given graph.

Since, the vertex \(a\) is connected directly to all the vertices except vertex \(c\). So, the color of vertices \(a\) and \(c\) can be same.

Similarly, no pair of vertices \(b,d\) and \(e\) is connected directly to each other. So, the color of vertices \(b,d\) and \(e\) can be same.

Therefore,

Vertex

Color

a

Green

b

Red

c

Green

d

Red

e

Red

Hence, \(2\) different colors are used to color the given graph. So, the chromatic number of the given graph is \(2\).

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