The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures

Štefan Gyürki, Mikhail Klin, Matan Ziv-Av

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper deals with the strongly regular graph T, having parameters (26, 10, 3, 4) and the largest possible automorphism group of order 120. The group G in its action on the vertex set of T has two orbits of length 20 and 6. Many special features of the graph T and its group G make it a remarkable object in algebraic graph theory. The presentation, arranged in the style of a tutorial, describes the graph T from many viewpoints of mathematics and computer algebra. Special attention is paid to the links of T with such classical structures as the Petersen graph, semi-icosahedron, icosahedron, dodecahedron, two-graphs on 26 points, Paley graphs, inversive plane and generalized quadrangles of order 5 and others.

Original languageEnglish
Title of host publicationIsomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016
EditorsGareth A. Jones, Ilia Ponomarenko, Jozef Širán
PublisherSpringer
Pages73-154
Number of pages82
ISBN (Print)9783030328078
DOIs
StatePublished - 1 Jan 2020
EventInternational workshop on Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016 - Pilsen, Czech Republic
Duration: 3 Oct 20167 Oct 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume305
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational workshop on Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016
Country/TerritoryCzech Republic
CityPilsen
Period3/10/167/10/16

Keywords

  • Algebraic graph theory
  • Antipodal graph
  • Association scheme
  • Block design
  • COCO
  • Coherent configuration
  • Computer algebra
  • Distance regular graph
  • Dodecahedron
  • Finite permutation group
  • GAP
  • Generalized quadrangle
  • Icosahedron
  • Inversive plane
  • Paley graph
  • Semi-icosahedron
  • Strongly regular graph
  • Two-graph
  • Weisfeiler–Leman stabilization

ASJC Scopus subject areas

  • Mathematics (all)

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