New strongly regular graphs from finite geometries via switching

Ferdinand Ihringer, Akihiro Munemasa

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We show that the strongly regular graph on non-isotropic points of one type of the polar spaces of type U(n,2), O(n,3), O(n,5), O+(n,3), and O(n,3) are not determined by its parameters for n≥6. We prove this by using a variation of Godsil-McKay switching recently described by Wang, Qiu, and Hu. This also results in a new, shorter proof of a previous result of the first author which showed that the collinearity graph of a polar space is not determined by its spectrum. The same switching gives a linear algebra explanation for the construction of a large number of non-isomorphic designs.

Original languageEnglish
Pages (from-to)464-474
Number of pages11
JournalLinear Algebra and Its Applications
Volume580
DOIs
Publication statusPublished - 2019 Nov 1

Keywords

  • Polar space
  • Spectrum
  • Strongly regular graph
  • Switching

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'New strongly regular graphs from finite geometries via switching'. Together they form a unique fingerprint.

Cite this