UGC-NET Computer Science July 2016 Solved Paper 2

UGC-NET Computer Science July 2016 Solved Paper 2

Q::2 The number of different spanning trees in complete graph, K₄ and bipartite graph, K_2,2 have ______ and _______ respectively.

 (1) 14, 14  (2) 16, 14

 (3) 16, 4    (4) 14, 4

Answer:: (3)

Explanation::

Let 'n' be total number of vertices in complete graph K_n then total different spanning trees are n^n-2 

n = 4 as given then total different spanning trees are 4^4-2 = 4² = 16.

The number of labelled spanning trees in a bipartite graph K_m,n is given by m^n-1*n^m-1 .
As given in question number of spanning trees in bipartite graph K_2,2 = 2^2-1 * 2^2-1 = 4.

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