since it is regular graph so max no. of edge
3n= 2e
as we know e = 2n – 3
equat both
3n/2 = 2n -4
n= 6 // no. of vertex
so no. of edges= 2n-3= 2*6-3= 12-3= 9
so using 6 vertex and 9 edges with every vertex has tree degree only two graph possible. one is k3,3