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A proper vertex colouring of a graph $G$ is a colouring of the vertices in $G$ in such a way that two vertices get different colours if they are adjacent. The minimum number of colours required for proper vertex colouring of $G$ is called the chromatic number of $G$. Then what is the chromatic number of the cycle graph on 149 vertices?
in Graph Theory by Veteran (104k points) | 270 views

4 Answers

+6 votes
As there are odd number of vertices in the cycle graph

So, Chromatic number will be 3
by Veteran (117k points)
+5 votes

THE FORMULA FOR CROMATIC NUM OF CYCLIC GRAPH IS

       N - 2(FLOOR(N/2))  + 2

EG : FOR TRIANGLE(3 CYCLE) WE NEED 3 COLOUR AND FORMULA GIVES   3(PUT N=3)

        FOR SQUARE(4 CYCLE) WE NEED =2 COLOURS AND FORMULA GIVES 2

FOR 149 IT WILL BE

              149-2(FLOOR(149/2))+2

            =149-2*74 +2 =149-148+2=3

 

by Boss (11k points)
+2 votes

For Cyclic Graph 
if no. of vertices = even then  Chromatic number is

if no. of vertices = odd then  Chromatic number is 3

by Active (2.9k points)
+1 vote
for odd no of vertices of cycle graph chromatic no is 3.
by Active (4k points)

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