If a graph had eight vertices of odd valence, what is the absolute minimum number of edges that would need to be duplicated to eulerize the graph?

Question

Quizplus · Accepted Answer

In order to eulerize a graph with eight vertices of odd valence, we need to add edges until all vertices have even valence. Since the sum of the degrees of all vertices in a graph is twice the number of edges, the eight vertices with odd valence contribute an odd sum of degrees. In order to make this sum even, at least four edges must be duplicated, which gives a total of 2*4=8 duplicated edges. Therefore, the answer is B, 4 duplicated edges.

If a Graph Had Eight Vertices of Odd Valence, What