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This is a probably a no brainer, and I've been searching but can't seem to find an answer. What is the term (and any alternate terms) for a graph with only two vertices and only one edge between them?

This is not a homework question :-)

+7  A: 

The complete graph on 2 vertices. Denoted K2. See: http://en.wikipedia.org/wiki/Complete_graph

adharris
I wouldn't say this is a standard but its the first thing that came to my mind.
job
Thanks for the edit Cory, looked for how to do subscripts, but I missed it.
adharris
+1  A: 

I don't know if an exact term exists, however it is a bipartite complete planar graph with 2 vertices for sure.

Jack
A: 

From further reading I found Regular Graph entry on wikipedia. It would seem to be a "1-regular graph", though there are other graphs which also qualify as such.

harschware