## Abstract

A finite collection of unit vectors S ⊂ ℝ^{n} is called a spherical two-distance set if there are two numbers a and b such that the inner products of distinct vectors from S are either a or b. We prove that if a ≠ -b, then a two-distance set that forms a tight frame for ℝ^{n} is a spherical embedding of a strongly regular graph. We also describe all two-distance tight frames obtained from a given graph. Together with an earlier work by S. Waldron (2009) [22] on the equiangular case, this completely characterizes two-distance tight frames. As an intermediate result, we obtain a classification of all two-distance 2-designs.

Original language | English |
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Article number | 13109 |

Pages (from-to) | 163-175 |

Number of pages | 13 |

Journal | Linear Algebra and Its Applications |

Volume | 475 |

DOIs | |

State | Published - Jun 2015 |

## Keywords

- Finite tight frames
- Spherical 2-designs
- Spherical designs of harmonic index 2
- Spherical two-distance sets
- Strongly regular graphs