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Computational Graph Theory Tree

Source: STEMS 2023 Maths CAT A Part A P6

January 8, 2023
graph theorySTEMSComputationalprobabilityalgebra

Problem Statement

There are 55 vertices labelled 1,2,3,4,51,2,3,4,5. For any two pairs of vertices u,vu, v, the edge uvuv is drawn with probability 1/21/2. If the probability that the resulting graph is a tree is given by pq\dfrac{p}{q} where p,qp, q are coprime, then find the value of q1/10+pq^{1/10} + p.
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