GateForum Test Series: Graph Theory - Graph Coloring

Question

The Chromatic Number of Cycle Graph with 7 vertices _____

Comments

Queston Says : "The Chromatic Number of Cycle Graph with 7 vertices _____"

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no bro, for cycle graph the chromatic number can either be 2 or 3

2 in case of  even node cycle graph and 3 for odd vertex cycle graph so answer should be 3 here. just draw a cycle graph and color each vertex so that all adjacent vertex will have different color.

Answer 1

For cyclic graph:

• If the number of vertices is odd then the chromatic number is $3$
• If the number of vertices is even then the chromatic number is $2$.

Ref: Cycle graph

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Thanks

Answer 2

Always remember for a K_n (complete graph) and C_2n+1 (Cycle graph with odd number of vertices), chromatic number is equal to (Maximum degree +1) - BROOK'S THEOREM.

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Thanks

Answer 3

if cycle graph, no.of vertices is even then chromatic no. is two because  represents minimum two colors and if no. of vertices is odd then chromatic no. is three because represents minimum three colors.

According to question no. of vertices is seven then chromatic no. is three.

Answer 4

A graph with no odd number of vertices cycle has chromatic number 1 or 2. Since this graph has odd number of vertices cycle, we can check starting from 3 that 3 satisfies.