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13.
Parameters of quotient-polynomial graphs
Herman, Allen ; Maleki, Roghayeh
Fiol has characterized quotient-polynomial graphs as precisely the connected graphs whose adjacency matrix generates the adjacency algebra of a symmetric association scheme. We show that a collection ...of non-negative integer parameters of size ▫$d + \frac{d(d-1)}{2}$▫ is adequate for describing symmetric association schemes of class ▫$d$▫ that are generated by the adjacency matrix of their first non-trivial relation. We use this to generate a database of the corresponding quotient-polynomial graphs that have small valency and up to 6 classes, and among these find new feasible parameter sets for symmetric association schemes with noncyclotomic eigenvalues.
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