# GATE | GATE CS 2020 | Question 62

Graph G is obtained by adding vertex s to K3,4 and making s adjacent to every vertex of K3,4. The minimum number of colours required to edge-colour G is _________ .

Note – This question was Numerical Type.
(A) 2
(B) 3
(C) 5
(D) 7

Answer: (D)

Explanation: Please note that question about edges color but not about vertices color.

So, according to edge coloring of a graph is an assignment of “colors” to the edges of the graph so that no two adjacent edges have the same color with an optimal number of colors.

There are minimum 4 colors required to color edges of graph K3,4, because maximum 4 edges are incident at some vertices.

For modified graph, 4 edges of differed color will be incident in vertex “s”, now from other set of 3 vertices of K3,4 will also be incident same vertex “s”. So, to preseve edge color property, we need 3 more colors for coloring this modified graph.

Hence, answer will be 4+3 = 7 colors.

Option (D) is correct.

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