An Euler circuit exits if and only if each vertex touches ______.
A)two edges
B)three edges
C)an even number of edges
D)an odd number of edges

Question

Quizplus · Accepted Answer

In an Euler circuit, we start at a vertex, travel to another vertex, and so on until we have traversed each edge exactly once and end up back where we started. For this to be possible, each time we enter a vertex, we must be able to leave that vertex by going through an unused edge. Therefore, each vertex must have an even number of edges, because we enter and leave a vertex through different edges.

An Euler Circuit Exits If and Only If Each Vertex