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The pseudo-cosine sequences of a distance-regular graph. (English) Zbl 1110.05105
Let $$\Gamma$$ be a distance-regular graph with diameter $$D$$, valency $$k$$ and intersection numbers $$a_{i}$$, $$b_{i}$$, $$c_{i}$$. Let $$\sigma _{0}$$, $$\sigma _{1}$$, $$\dots$$, $$\sigma _{D}$$ and $$\rho _{0}$$, $$\rho _{1}$$, $$\dots$$, $$\rho _{D}$$ denote two pseudo-cosine sequences of $$\Gamma$$. This pair of sequences is called tight whenever $$\sigma _{0}\rho _{0}$$, $$\sigma _{1}\rho _{1}$$, $$\dots$$, $$\sigma _{D}\rho _{D}$$ is a pseudo-cosine sequence of $$\Gamma$$. By definition $$\sigma _{0}$$, $$\sigma _{1}$$, $$\dots$$, $$\sigma _{D}$$ is called a pseudo-cosine sequence of $$\Gamma$$ if $$\sigma _{0}=1$$ and $$c_{i}\sigma _{i-1}+a_{i}\sigma _{i}+b_{1}\sigma _{i+1}=k\sigma _{1}\sigma _{i}$$ holds for every $$1\leq i\leq D-1$$. The authors find all the tight pairs of pseudo-cosine sequences of $$\Gamma$$.

##### MSC:
 5e+30 Association schemes, strongly regular graphs
##### Keywords:
association scheme; pseudo-cosine sequence
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##### References:
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