Every graph with an Euler circuit has only vertices with even valences.

Question

Quizplus · Accepted Answer

This statement is true. An Euler circuit is a circuit that visits every edge of a graph exactly once and returns to the starting vertex. In such a circuit, every time a vertex is visited, an edge is used to enter that vertex and another edge is used to exit that vertex. Therefore, every vertex in an Euler circuit must have an even degree, since each edge incident to the vertex contributes to the degree of the vertex twice.

Every Graph with an Euler Circuit Has Only Vertices with Even