UGC-NET | UGC NET CS 2016 July – II | Question 2

The number of different spanning trees in complete graph, K4 and bipartite graph, K2,2 have ______ and _______ respectively.
(A) 14, 14
(B) 16, 14
(C) 16, 4
(D) 14, 4


Answer: (C)

Explanation: Spanning trees in complete graph is equal to n(n-2)(where n is no of sides or regularity in complete graph).
So, spanning trees in complete graph K4 will be 4(4 – 2).
i.e. 42 = 16.
Spanning trees in a bipartite graph Km,n is equal to m(n-1) * n(m-1).
So, spanning trees in K2,2 will be 2(2-1) * 2(2-1).
i.e. 21 * 21.= 4.
So, option (C) is correct.

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