Thread: question in math logic

If we have K_n denote the complete graph on n vertices, can any one explain to me how to know how many substructures does K_n have?

Originally Posted by Mike12

If we have K_n denote the complete graph on n vertices, can any one explain to me how to know how many substructures does K_n have?

What do you mean by substructure?

If B is a set, then A ⊂ B means that A is a subset of B.
If N is a structure, then M ⊂ N means that M is a substructure of N.

Originally Posted by Mike12

If B is a set, then A ⊂ B means that A is a subset of B.
If N is a structure, then M ⊂ N means that M is a substructure of N.

So in this context, a substructure would be a subgraph of .

Are these labeled or unlabeled graphs?

there is no thing about labeled or unlabeled graph , all what I have in the question is a complete graph

If N is a structure, then M ⊂ N means that M is a substructure of N.

And what does ⊂ mean when applied to two structures? After all, structures are not just sets; they are tuples consisting of the domain together with functions and/or relations. Therefore, the regular concept of set inclusion cannot be applied to structures, and a specific definition is needed.

According to Wikipedia, M is a substructure of N if the domain of M is a subset of the domain of N and the relations of M are the corresponding relations of N restricted to the domain of M. A subgraph is a not necessarily a substructure because it may fewer edges than what is inherited from the large graph. Subgraphs are called weak substructures. So, a relevant question about this problem is, are we talking about regular or weak substructures? Or what is the definition of a substructure?

I think in this question it means subgraph

Originally Posted by Mike12

I think in this question it means subgraph

If we have vertices then has edges.

There are possible subgraphs of .
(That counts the empty-edge subgraph).

Would tell us what textbook you are following?

It is (mathematical logic) , so you told me that there are two to the power N choose 2 possible subgraphs.

Originally Posted by Mike12

It is (mathematical logic) , so you told me that there are two to the power N choose 2 possible subgraphs.

I answered a Graph Theory problem.
I have no idea how that relates to mathematical logic. You seem to refuse to answer a simple question about the text material. If you tell us about the textbook, one of us may have a better idea as to what you are doing. Until then, I done with it.

sorry but I do not refuse to answer you about textbook , the text book is ( Mathematical logic).