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

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Official answer: 16 (±0)

Graph Theory

According to Cayley's Formula, the number of spanning trees in a labeled complete graph $K_n$ with $n$ vertices is given by:

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

For $n = 4$ :

4^{4-2} = 4^2 = 16

Thus, the total number of spanning trees is 16.

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This Graph Theory previous year question is Q34 of the GATE CSE 2024 Set 1 paper. Find more GATE CSE PYQs on Graph Theory in Engineering Mathematics, or browse all GATE CSE PYQs.

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Graph Theory has 21 GATE CSE PYQs across 14 papers from 2012 to 2026. 3 of them are 1-mark NAT questions like this one, and GATE CSE 2024 Set 1 has 3.

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