Let v = { 1,2,3,4,5} be the set of vertices.How amny different graphs can be made with 'V' as set of vertices?
Solution provided says that we can make 2^10 graphs ( without self loops).
Does that make sense?
Well it depends on what is meant by a graph.
$\displaystyle \binom{5}{2}=10$ so on five vertices there are ten simple edges possible.
In a directed graph each edge can have one of two directions (no two-way edges in a simple directed graph).
In that case the answer is infact $\displaystyle 2^{10}$.
I was trying to make sense of the provided answer.
It seems they are assumming a complete simple graph on five vertices.
Then giving a direction to each edge.
Otherwise, that answer does not work.
Because there are $\displaystyle 2^{10}$ simple non-directed graphs on five vertices.
So there would be more directed graphs.
I did say it depends on the definitions used.