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A complete undirected graph of n nodes can have maximum ______ spanning trees.(a) n^n+1(b) n^n-2(c) \(\frac{n(n+1)}{2}\)(d) nThe question was posed to me during an online exam.Enquiry is from Spanning Trees topic in chapter Trees of Discrete Mathematics

Answer»

The correct OPTION is (b) n^n-2

The explanation is: The spanning TREE does not CONTAIN any cycle. If a spanning tree has n nodes, there are n-1 edges. A COMPLETE graph can have a maximum of n^n-2number of spanning trees.



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