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Krein parameters and antipodal tight graphs with diameter 3 and 4. (English) Zbl 1024.05086
Authors’ abstract: We determine which Krein parameters of nonbipartite antipodal distance-regular graphs of diameter 3 and 4 can vanish, and give combinatorial interpretations of their vanishing. We also study tight distance-regular graphs of diameter 3 and 4. In the case of diameter 3, tight graphs are precisely the Taylor graphs. In the case of antipodal distance-regular graphs of diameter 4, tight graphs are precisely the graphs for which the Krein parameter $$q^1_{11}$$ vanishes.

##### MSC:
 5e+30 Association schemes, strongly regular graphs
##### Keywords:
distance-regular graphs; Taylor graphs
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