The number of vertices in an undirected graph with odd degree is always _____.

In any undirected graph, the sum of the degrees of all vertices is equal to twice the number of edges. This sum is always even.

Let the number of vertices with odd degree be k. The sum of degrees of these k vertices is the sum of k odd numbers.

The sum of an odd number of odd integers is odd, while the sum of an even number of odd integers is even.

Since the total sum of degrees must be even, the sum of odd-degree vertices must also be even. Therefore, k must be even.

Hence, the number of vertices with odd degree is always an even number.