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Manipal MET2017MathematicsMathematical Induction

For what values of n is the graph K_n Eulerian?

Options

  1. AOdd values of n
  2. BEven values of n
  3. CBoth odd and even values of n
  4. DNone of the above

Correct answer

A. Odd values of n

Step-by-step 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.

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