English

Complex Two-Graphs via Equiangular Tight Frames

Combinatorics 2017-03-16 v2

Abstract

In `A survey of two-graphs' \cite{Sei}, J.J. Seidel lays out the connections between simple graphs, two-graphs, equiangular lines and strongly regular graph. It is well known that there is a one-to-one correspondence between regular two-graphs and equiangular tight frames. This article gives a generalization of two-graphs for which these connections can be mimicked using roots of unity beyond ±1\pm 1.

Keywords

Cite

@article{arxiv.1408.0334,
  title  = {Complex Two-Graphs via Equiangular Tight Frames},
  author = {Thomas Hoffman and James Solazzo},
  journal= {arXiv preprint arXiv:1408.0334},
  year   = {2017}
}

Comments

The current definition on page 11 of mth root two graphs is wrong. We can quickly fix it for prime roots of unity, but the more general case does not work. We are not sure at the moment how many of the following results might be impacted and we don't want this work to be misleading to others

R2 v1 2026-06-22T05:18:53.792Z