For v=4 vertices, there must be 7 possible graphic sequence (3,3,3,3)(3,3,2,2)(3,2,2,1)(3,1,1,1)(2,2,2,2)(2,2,1,1)(1,1,1,1). From (3,3,3,3), one simple graph(complete) can be found. From(3,3,2,2), 6 simple connected graphs are possible,From (2,2,1,1), 12 simple connected graphs are possible.
Then how can I determine all simple connected labeled graphs for degree sequence $d_{i}= d_{1},d_{2},...,d_{n} \forall i=1,n $. Is there any formula or equation exist for the same?