JT's

An Euler trail is a walk that uses every edge of a graph exactly once. An Euler circuit is a circuit that uses every edge of a graph exactly once. A Euler trail with same endpoints is a Euler circuit. Here are some examples: Letbe a finite connected graph and denote the number of vertices that have odd degrees. Prove that G has a Euler trail if and only if . First, by the Handshake Theorem, we c..