GATE | GATE-CS-2004 | Question 77

The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same colour, is

(A) 2
(B) 3
(C) 4
(D) 5

Answer: (C)

Explanation: graph coloring

Two vertices are said to be adjacent if they are directly connected, i.e., there is a direct edge between them.
So, here, we can assign same color to 1 & 2 (red), 3 & 4 (grey), 5 & 7 (blue) and 6 & 8 (brown).
Therefore, we need a total of 4 distinct colors.

Thus, C is the correct choice.


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