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Peer-reviewedCC BY-NC-NDDiscrete Mathematics

Complex Hadamard matrices and strongly regular graphs

  • Ada Chan1
  1. 1York University
Open at sourceDOICite

Abstract

In 1970, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph X contains a Hadamard matrix then X is either of Latin square type or of negative Latin square type. We extend their result to complex Hadamard matrices and find only three additional families of parameters for which the strongly regular graphs have complex Hadamard matrices in their adjacency algebras. Moreover we show that there are only three distance regular covers of the complete graphs that give complex Hadamard matrices.

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Cite

BibTeXRIS
BibTeX
@article{chan2026complex,
  title = {{Complex Hadamard matrices and strongly regular graphs}},
  author = {Ada Chan},
  journal = {Discrete Mathematics},
  year = {2026},
  month = jun,
  doi = {10.1016/j.disc.2026.115297},
  url = {https://doi.org/10.1016/j.disc.2026.115297},
  note = {CC BY-NC-ND},
}
RIS
TY  - JOUR
TI  - Complex Hadamard matrices and strongly regular graphs
AU  - Ada Chan
PY  - 2026
DA  - 2026/06/26
JO  - Discrete Mathematics
DO  - 10.1016/j.disc.2026.115297
UR  - https://doi.org/10.1016/j.disc.2026.115297
AB  - In 1970, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph X contains a Hadamard matrix then X is either of Latin square type or of negative Latin square type. We extend their result to complex Hadamard matrices and find only three additional families of parameters for which the strongly regular graphs have complex Hadamard matrices in their adjacency algebras. Moreover we show that there are only three distance regular covers of the complete graphs that give complex Hadamard matrices.
SN  - 0012-365X
SN  - 1872-681X
ER  -