The Full Question
Find all(loop-free) non-isomorphic, undirected graphs with four vertices. How many of these graphs are connected?
I'm a little infuriated at this question because it is supposed to be easy, but I can't seem to crack it. I suppose we must have 4 vertices, so I could go through all graphs with zero edges, 1 edges, 2 edges, 3 edges, etc. This seems like it might go on for a long time(i.e. the rest of my natural life). I suppose we may reach a point where all I can make is loops if I add more edges?(I have no idea where this would be) Could anyone maybe offer me a helping hand with this question? I'm fairly confused