Question

Find all non isomorphic graphs of order 5.

Now here is the issue, I know I need to find graphs of size 0-5 then just multiply by 2 for the total number of graphs because each has a complement. Thanks to OEIS I know there are 34 total, but how do I find all of them? How do I develop all of the possibilities for lets say a graph of size 4?

Answer 1

http://mathoverflow.net/questions/29593/non-isomorphic-graphs-of-given-order

Answer 2

unfortunately, that does not really help here. thank you though

Answer 3

Once I have the 17 graphs of order 5-0, I can easily get the other 17 by their complements. Now m=0,1 are obvious

Answer 4

The issue comes when I have 4 edges or 5, how do I know if I have found them all?

Answer 5

the m=5 graphs will be self-complementary, no?

Answer 6

Connected or not?

Answer 7

What do you mean by connected?

Answer 8

Every graph is order 5, the size varies from 0 to the komplete graph of 10

Answer 9

What do you mean by order? Is order the number of vertices?

Answer 10

yea

Answer 11

oh, 0 edges implies 1 graph 1 edge imples 1 graph 2 edges implies 2 graphs 3 edges implies 6? graphs? I am not sure.

Answer 12

Do the graph need to be connected?

Answer 13

...?

Answer 14

Can you show me the graphs of order m = 0 , 1, and possibly a couple of order 2 so I get an idea of what you're looking for? It seems like you're trying to find a way to generate all possible combinations of some edges and vertices, right? But I'm not sure I know what restrictions you have like if they can be connected twice, if it's a directed graph, etc

Answer 15

That is order 5 and size 0

Answer 16

Everything else is isomorphic to that

Answer 17

However, those are all of the graphs I can come up with, for size 2

Answer 18

oops deleted this one for m=2

Answer 19

Here's part of a strategy I'm developing. I haven't considered how to remove the graphs for any m that exceed the order (for example 3 separate lines connecting is m=3 and order 6 graph).

But when you are looking for shapes you only have to look for single connected shapes and then all the other graphs for say m=5 will be also include the total number of the lower sets as well combined, so the union of m=4 and m=1, so if we let these numbers stand for the number of graphs in m instead of being actual numbers, we have 5*0 + 4*1+3*2+2*2*1+ 3*1*1+2*1*1*1+1*1*1*1*1 possible graphs for m=5, however we need to cut this down to remove all the order 6 and up ones.

Answer 20

I know that there are 34 graphs, it's not the number, it's just figuring that out without using OEIS

Answer 21

order 5 only.