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

Štefan Gyürki; Mikhail Klin; Matan Ziv-Av

doi:10.1007/978-3-030-32808-5_4

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

Štefan Gyürki, Mikhail Klin, Matan Ziv-Av

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016
Editors	Gareth A. Jones, Ilia Ponomarenko, Jozef Širán
Publisher	Springer
Pages	73-154
Number of pages	82
ISBN (Print)	9783030328078
DOIs	https://doi.org/10.1007/978-3-030-32808-5_4
State	Published - 1 Jan 2020
Event	International workshop on Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016 - Pilsen, Czech Republic Duration: 3 Oct 2016 → 7 Oct 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	305
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International workshop on Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016
Country/Territory	Czech Republic
City	Pilsen
Period	3/10/16 → 7/10/16

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

General Mathematics

Access to Document

10.1007/978-3-030-32808-5_4

Cite this

Gyürki, Š., Klin, M., & Ziv-Av, M. (2020). The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures. In G. A. Jones, I. Ponomarenko, & J. Širán (Eds.), Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016 (pp. 73-154). (Springer Proceedings in Mathematics and Statistics; Vol. 305). Springer. https://doi.org/10.1007/978-3-030-32808-5_4

Gyürki, Štefan ; Klin, Mikhail ; Ziv-Av, Matan. / The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures. Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016. editor / Gareth A. Jones ; Ilia Ponomarenko ; Jozef Širán. Springer, 2020. pp. 73-154 (Springer Proceedings in Mathematics and Statistics).

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title = "The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures",

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.",

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",

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Gyürki, Š, Klin, M & Ziv-Av, M 2020, The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures. in GA Jones, I Ponomarenko & J Širán (eds), Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016. Springer Proceedings in Mathematics and Statistics, vol. 305, Springer, pp. 73-154, International workshop on Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016, Pilsen, Czech Republic, 3/10/16. https://doi.org/10.1007/978-3-030-32808-5_4

The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures. / Gyürki, Štefan; Klin, Mikhail; Ziv-Av, Matan.
Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016. ed. / Gareth A. Jones; Ilia Ponomarenko; Jozef Širán. Springer, 2020. p. 73-154 (Springer Proceedings in Mathematics and Statistics; Vol. 305).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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.

AB - 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.

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KW - Inversive plane

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Gyürki Š, Klin M, Ziv-Av M. The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures. In Jones GA, Ponomarenko I, Širán J, editors, Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016. Springer. 2020. p. 73-154. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-32808-5_4

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

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this