P-polynomial table algebras and distance-regular graphs
Hein, Robert J.
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It is shown that given a standard, integral, P-polynomial table algebra with integer dual degrees, with valency k > 2 and with intersection array that has one column repeated g times, then the diameter d is bounded by a function of (d —g) and k. Also a classification of all homogeneous, monotonic, standard, P-polynomial table algebras is shown, and it is determined which of these table algebras are integral and have integer dual degrees. In particular, it is shown that this is the case only if d = 2. It is noted that some of these algebras come from association schemes and some do not.