Question

no of simple graph possible with 6 vertices and 4 edges is ?

Comments

Check this : https://math.stackexchange.com/questions/1072726/counting-simple-connected-labeled-graphs-with-n-vertices-and-k-edges

Answer 1

6 vertices uses 12 edges given then using this data every graph has even length cycle occurs...
So it is bipartite graph and we know bipartite graph has chromatic number is 2...
So only 2 number of simple graphs possible