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.
Here are facts.
Originally Posted by demon1
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.