While I understand your question, I am still puzzled by it.
Do you understand that given any simple graph, , then (complement) is connected?
I cannot see how any list could help.
Does anyone know where I can find a table that displays all connected graphs up to some order? (Of course the higher the better). For example there is this nice table of prime knots and links http://www.math.unl.edu/~mbrittenham2/ldt/table9.gif and any thing like that would be awesome.
I'm doing starting some research on graph theory and this would be good to have a round as reference. Thanks in advance guys
The list will help me because for what I am doing it is quite pointless to study disconnected graphs as their properties (for this situation) can quite easily be derived from their components. Having a list of connected graphs will save me the trouble of finding those graphs for studying.
If it helps, I just want a large variety of low order graphs so that I can play with them myself and gain intuition into the problem I have.
Anyhow, It would still be useful to have a table of connected graphs such that each element is not isomorphic to another. I just don't want to create the list myself if someone already has...