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GATE CSE 2024 Session 1 Q34: Number of spanning trees of K4

Question

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

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 16 (official GATE 2024 final answer key)

Concept used: Cayley's formula: KnK_n has nn−2n^{n-2} labelled spanning trees.

First step: Apply nn−2n^{n-2} with n=4n = 4.

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key