Maximality of Seidel matrices and switching roots of graphs

2021/02/24 by Meng-Yue Cao, Cao, Meng-Yue, Jack H. Koolen +5 · 1 citation
Computer Science · Mathematics · #05C22 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2102.11989

openalex publication_date 2021/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \arccos1/3. 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.

Cited by

• Biangular lines with angles arccos(1/5) and arccos(3/5)

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