Moore bound

Moore bound

An upper limit on the number of nodes in a regular graph of degree d>2 and diameter k:

N(d,k) <= d(d-1)^k - 2 ------------ d-2
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By the well-known Moore bound for graphs or digraphs of diameter two we know that f has to increase at least as fast as [square root of n].
By the Moore bound for diameter two, the probability of a random Cayley digraph of degree k and order n (for a general group) having diameter 2 is zero if k < [[square root of n]].
In 2001 his sculpture Henry Moore Bound to Fall broke records when it was sold for a reported $US9.