Triangles in labelled cubic graphs
No cubic graph has an odd number of points. A method is found of calculating the number tp of labelled connected cubic graphs with 2p points rooted at a triangle. The method presupposes knowledge of the numbers qk of labelled connected cubic graphs with 2k points and k<p. Labelled connected cubic graphs have already been counted by Read, so this allows determination of the mean number tp/qp of triangles in a labelled connected cubic graph with 2p points, for all p>1. It is shown that tp/qp → 4/3 as p → ∞.
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