Question

For what values of n is the graph $K_n$ Eulerian?

• A. Odd values of n
• B. Even values of n
• C. Both odd and even values of n
• D. None of the above

Hint:

Eulerian circuit exists iff all vertices have even degree.

Answer 1

The Correct Option is B

Step 1: $K_n$ is Eulerian if all vertices have even degree. In $K_n$, degree of each vertex = $n-1$.}
Step 2: $n-1$ is even when $n$ is odd. So $K_n$ is Eulerian for odd $n$. Option (A) is correct.}