Table of Connected Graphs

Apr 2010
21
0
Florida
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 (Bow)
 

Plato

MHF Helper
Aug 2006
22,462
8,634
While I understand your question, I am still puzzled by it.
Do you understand that given any simple graph, \(\displaystyle G\), then \(\displaystyle G\text{ or }G^c\)(complement) is connected?
I cannot see how any list could help.
 
Apr 2010
21
0
Florida
Not quite...

While I understand your question, I am still puzzled by it.
Do you understand that given any simple graph, \(\displaystyle G\), then \(\displaystyle G\text{ or }G^c\)(complement) is connected?
I cannot see how any list could help.
This is not true as \(\displaystyle (K_2\cup K_2)^c\cong K_2\cup K_2\) both of which are clearly disconnected. It may be the case that this is the only example, but since I am not sure I won't jump to conclusions.

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.
 

Plato

MHF Helper
Aug 2006
22,462
8,634
We must be using different definitions of complement and/or union of graphs.
That statemenent is a well-known property of simple graphs.
 

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Apr 2010
21
0
Florida
We must be using different definitions of complement and/or union of graphs.
That statemenent is a well-known property of simple graphs.
Oh wow... my bad. This is definitely true now that I think about it. For some reason I missed the middle cross when computing the complement. My apologies.

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...