GATE CS 2024 Set 1 Q.34: Graph Theory

The number of spanning trees in a complete graph of 4 vertices labelled A, B, C, and D is _________

Your answer

Official answer and solution

Solution

Apply Cayley's formula $n^{n-2}$ for the number of spanning trees in a labelled complete graph $K_n$ .

By Cayley's formula, the number of spanning trees in a complete graph $K_n$ on $n$ labelled vertices is $n^{n-2}$ . For $n = 4$ :

\text{Number of spanning trees} = 4^{4-2} = 4^2 = 16

Final answer

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