GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
71 views
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?
asked in Graph Theory by Veteran (76k points)   | 71 views

3 Answers

+2 votes
As there are odd number of vertices in the cycle graph

So, Chromatic number will be 3
answered by Veteran (52.4k points)  
+1 vote

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

 

answered by Boss (9.6k points)  
0 votes
for odd no of vertices of cycle graph chromatic no is 3.
answered by Loyal (3.1k points)  


Top Users Mar 2017
  1. rude

    4272 Points

  2. sh!va

    2994 Points

  3. Rahul Jain25

    2804 Points

  4. Kapil

    2608 Points

  5. Debashish Deka

    2244 Points

  6. 2018

    1414 Points

  7. Vignesh Sekar

    1338 Points

  8. Akriti sood

    1246 Points

  9. Bikram

    1246 Points

  10. Sanjay Sharma

    1016 Points

Monthly Topper: Rs. 500 gift card

21,452 questions
26,771 answers
60,972 comments
22,985 users