eulerian graph

Prove or disprove: There is no Eulerian graph with an even number of vertices and an odd number of edges.



from what i understand i think this statement is true. u cant have an eulerian graph with an even number of vertices and an odd number of edges. but im not sure how to prove this.

Quote:

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Originally Posted by demon1

Prove or disprove: There is no Eulerian graph with an even number of vertices and an odd number of edges.

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Here are facts.
If a graph is Eulerian then it is connected and each vertex is even.
The degree sum is twice the number of edges.
An even number times an even number is a multiple of four.

Now you can prove it by putting those together.