... applications of these polynomials, deriving new bounds for the radius of agraph and the “weight k-excess” of a vertex. Generalizing these results, and groupingideas of Van Dam [10] , and Garriga and ... presence of high levels of structure in the consideredgraphs. See, for instance, the papers of Haemers and Van Dam, [12] , and Garriga,Yebra, and the author [17] ,[18] ,[20] ,[21] , and also ... Doob, and Sachs [9] , and the comprehensive text about distance-regular graphs of Brouwer,Cohen and Neumaier [5] . (See also the surveys of Cvetkovi´c and Doob [8] and Schwenk and Wilson [38] .)...