I want to make sure I understand the definition of an Eulerian Graph / Trail / Cycle / Circut.
I'm reading Schaum's Discrete Mathematics Outline which gives the following definitions:
A graph G is called an Eulerian Graph if there exists a closed traversable trail, called an Eulerian trail.
It then goes on to say that:
A finite connected graph is Eulerian if and only if each vertex has even degree.
I then read the following in Wikipedia:
Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree
...not every Eulerian graph possesses an Eulerian cycle
So which one is right? Can a graph be Eulerian, having only vertices of even degree, yet not contain an Eulerian circuit?
Also, isn't there a distinction between an Eulerian trail and an Eulerian Cycle / Circuit?