Self Doubt

Question

How many distinct unlabelled simple graphs (connected or disconnected), having n nodes, are possible?

Comments

labeled or unlabeled nodes ?

if vertices are labeled, then, total no. of edges possible = $\binom{n}{2}=\frac{n(n-1)}{2}$ =E

total no of graphs possible are $\sum \binom{E}{i}$ , i={0,1,2,3....E} //i.e taking 0,1,2,3..... edges at a time.

but if vertices are unlabeled, there is no perticular formula generating total # of graphs, you have to find it maually

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@joshi_nitish

I was asking for unlaballed nodes.

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for unlabelled, there does not exist any perticular formula.

Answer 1

i think it is equal to...2^(nC2)...

as total no. of possible edges with n vertices are ..nC2....

...and every edges has two chance ...either it may or may not be involve in the graph...??

Comments

Yeah, that's true about labelled but not for unlabelled graph