Question

What is the chromatic number of the complete graph $K_n$?

• A. One
• B. Four
• C. \(\dfrac{n}{2}\)
• D. \(n\)

Hint:

Complete graphs require unique colors for each vertex since all are interconnected.

Answer 1

The Correct Option is D

In a complete graph \(K_n\), every vertex is connected to every other vertex. Hence, no two vertices can share the same color. Thus, \(n\) colors are needed — one for each vertex.