Equiangular line systems and switching classes containing regular graphs

Abstract

We develop the theory of equiangular lines in Euclidean spaces. Our focus is on the question of when a Seidel matrix having precisely three distinct eigenvalues has a regular graph in its switching class. We make some progress towards an answer to this question by finding some necessary conditions and some sufficient conditions. Furthermore, we show that the cardinality of an equiangular line system in $18$ dimensional Euclidean space is at most $60$.

17 pages

References in corpus (3)

• Equiangular lines in Euclidean spaces
• Upper bounds for $s$-distance sets and equiangular lines
• There is no (95,40,12,20) strongly regular graph

Cited by in corpus (10)

• On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix
• $k$-point semidefinite programming bounds for equiangular lines
• Open problems in the spectral theory of signed graphs
• Equiangular lines, Incoherent sets and Quasi-symmetric designs
• Real equiangular lines in dimension 18 and the Jacobi identity for complementary subgraphs
• The Lemmens-Seidel conjecture and forbidden subgraphs
• A remark on a construction of D.S. Asche
• Maximality of Seidel matrices and switching roots of graphs
• Enumeration of Seidel matrices
• Some Remarks on Systems of Equiangular Lines