The Lemmens-Seidel conjecture and forbidden subgraphs

Meng Yue Cao, Jack H. Koolen*, Yen Chi Roger Lin, Wei Hsuan Yu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper we show that the conjecture of Lemmens and Seidel of 1973 for systems of equiangular lines with common angle arccos⁡(1/5) is true. Our main tool is forbidden subgraphs for smallest Seidel eigenvalue −5.

Original languageEnglish
Article number105538
JournalJournal of Combinatorial Theory. Series A
Publication statusPublished - 2022 Jan


  • Equiangular lines
  • Forbidden subgraphs
  • Pillar method
  • Seidel matrices

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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