preprint · ArXiv.org · 2003

The Pseudo Cosine Sequences of a Distance-Regular Graph

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Abstract

Let $G$ denote a distance-regular graph with diameter $D\ge 3$, valency $k$, and intersection numbers $a_i$, $b_i$, $c_i$. By a {\it pseudo cosine sequence} of $G$ we mean a sequence of real numbers $s_0, s_1, ..., s_D$ such that $s_0=1$ and $c_i s_{i-1}+a_i s_i+b_i s_{i+1}=k s_1 s_i$ for $ 0 \le i \le D-1$. Let $s_0, s_1,..., s_D$ and $p_0, p_1, ..., p_D$ denote pseudo cosine sequences of $G$. We say this pair of sequences is {\it tight} whenever $s_0 p_0, s_1 p_1, ..., s_D p_D$ is a pseudo cosine sequence of $G$. In this paper, we determine all the tight pairs of pseudo cosine sequences of $G$.

Cite this paper

APA 7

Pascasio, A. A., & Terwilliger, P. (2003). The Pseudo Cosine Sequences of a Distance-Regular Graph. ArXiv.org. https://doi.org/10.48550/arxiv.math/0312150

MLA 9

Pascasio, Arlene A., and Paul Terwilliger. “The Pseudo Cosine Sequences of a Distance-Regular Graph.” ArXiv.org, 2003, https://doi.org/10.48550/arxiv.math/0312150.

Chicago

Pascasio, Arlene A., and Paul Terwilliger. 2003. “The Pseudo Cosine Sequences of a Distance-Regular Graph.” ArXiv.org. https://doi.org/10.48550/arxiv.math/0312150.

Harvard

Pascasio, A.A. and Terwilliger, P. (2003) ‘The Pseudo Cosine Sequences of a Distance-Regular Graph’, ArXiv.org. Available at: https://doi.org/10.48550/arxiv.math/0312150.

BibTeX

@misc{pascasio2003pseudo,
  title = {{The Pseudo Cosine Sequences of a Distance-Regular Graph}},
  author = {Pascasio, Arlene A. and Terwilliger, Paul},
  journal = {ArXiv.org},
  year = {2003},
  doi = {10.48550/arxiv.math/0312150}
}

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