Maximality of Seidel matrices and switching roots of graphs

Meng Yue Cao, Jack H. Koolen, Akihiro Munemasa, Kiyoto Yoshino

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we discuss maximality of Seidel matrices with a fixed largest eigenvalue. We present a classification of maximal Seidel matrices of largest eigenvalue 3, which gives a classification of maximal equiangular lines in a Euclidean space with angle arccos 1 / 3. Motivated by the maximality of the exceptional root system E8, we define strong maximality of a Seidel matrix, and show that every Seidel matrix achieving the absolute bound is strongly maximal.

Original languageEnglish
JournalGraphs and Combinatorics
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Adjacency matrices
  • Seidel matrices
  • Switching classes of graphs
  • Two-graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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