Let X and Y be the integers representing the number of simple graphs possible with 3 labeled vertices and 3 unlabeled vertices respectively. Let X – Y = N. Then, find the number of spanning trees possible with N labeled vertices complete graph.
(A) 4
(B) 8
(C) 16
(D) 32
Answer: (C)
Explanation: Number of simple graphs possible with n labeled vertices is 2^(n(n-1)/2).
Number of simple graphs possible with n unlabeled vertices is n+1.
Number of spanning tree possible with n vertices complete graph n^(n-2)
X =8
Y = 4
X-Y=4
Therefore required answer is 4^2=16.