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If each and every vertex in G has degree at most 23 then G can have a vertex colouring of __________

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If each and every vertex in G has degree at most 23 then G can have a vertex colouring of __________

(a) 24

(b) 23

(c) 176

(d) 54

This question was posed to me during an online interview.

Question is from Graphs Properties in section Graphs of Discrete Mathematics

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Correct choice is (a) 24

Explanation: A vertex colouring of a graph G = (V’,E’) with m colours is a mapping f:V’ -> {1,…,m}  such that f(u)!=f(v) for every (u,v) belongs to E’. Since in worst case the graph can be complete, d+1 colours are necessary for graph containing vertices with degree at most ‘d’. So, the required answer is 24.

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