Q106 / 170 · Manipal (MET) 2017 · Mathematics

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

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

Solution

We know that $K_n$, the complete graph of $n$ vertices is a connected graph in which degree of each vertex is $n-1$. Since, a graph is Eulerian if and only if it is connected and degree of each vertex is even, we conclude that $K_n$ is an Euler graph if and only if $n$ is odd.

Hence, the correct answer is option: 'A'.

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