A finite graph G has an even number of vertices with odd valency. Theorem: A finite graph G has an even number of vertices with odd valency. Now, I draw a finite graph : !enter image description here The number of vertices is 4. And Degree(1) = 1, Degree(2) = 2, Degree(3) = 2, Degree(4) = 1. But the theorem say : **Each vectices with odd valency**. And I see degree of 2 and 3 are 2. I don't understand it. Can you expland it?

The correct interpretation should be "If $G$ is a finite graph, then the number of vertices with odd valency is even."

You're interpreting it as "If $G$ is a finite graph with an even number of vertices, then each vertex has odd valency."