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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With stable-jockey Ryan Moore bound for Churhcill Downs to ride Mendelssohn in Saturday's Kentucky Derby, riding arrangements for the Ballydoyle colts at Newmarket will be watched with interest.
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].
In 2001 his sculpture Henry Moore Bound to Fall broke records when it was sold for a reported $US9.9m.