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An inequality on the cosines of a tight distance-regular graph. (English) Zbl 0979.05112
The author considers a distance-regular graph $$\Gamma$$ with diameter $$d\geq 3$$, valency $$k$$, and eigenvalues $$k=\theta_0>\theta_1>\cdots>\theta_d$$, which is tight in the sense of A. Jurišić, J. Koolen, and P. Terwilliger [J. Algebr. Comb. 12, No. 2, 163-197 (2000; Zbl 0959.05121)]. He obtains an inequality involving the first, second and third cosines associated with $$\theta$$, when $$\theta$$ is $$\theta_1$$ or $$\theta_d.$$ ($$\theta_1$$ and $$\theta_d$$ are involved in the definition of a tight graph.) Also, the author proves that equality is attained if and only if $$\Gamma$$ is dual biparite $$\mathcal Q$$-polynomial with respect to $$\theta$$.

##### MSC:
 5e+30 Association schemes, strongly regular graphs
Full Text:
##### References:
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