Undirected graphs


How many undirected graphs can be constructed out of a given set V={v1, v2… vn} of n vertices


For given n no of vertices ,
Total no of possible edges =n*(n-1)/2 .
Now, for every edge, there are to possible options, either we pick it or don’t pick.
So total number of possible graphs is 2n(n-1)/2.


In an undirected graph, there can be maximum of n(n-1)/2 edges. We can choose to have (or not have) any of the n(n-1)/2 edges.
So, total number of undirected graphs with n vertices is


Total no of possible edges=n(n-1)/2