Thread: QUESTION about complete graph

1. Fix n ≥ 3 to be an integer. How many graphs are there that aresub-graphs of Kn (assume that all nodes are different and included in the sub-graph)?
   
   Thanks Brothers !
   

Originally Posted by kakatomy

Fix n ≥ 3 to be an integer. How many graphs are there that are sub-graphs of Kn (assume that all nodes are different and included in the sub-graph)?

I not sure that I understand that statement.

There are non-empty subsets of vertices.

If we chose a subset of vertices and include any edge between any two of them, then that is the number of sub-graphs.

Now some authors do not allow single vertex sub-graphs.
In that case we use the number

Hi, if that is the wording of your problem, with the "fix ," then I think something is missing, because the solution does not depend on at all. Do you mean connected subgraphs? Do you include the order-zero graph?