TY - GEN

T1 - The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures

AU - Gyürki, Štefan

AU - Klin, Mikhail

AU - Ziv-Av, Matan

N1 - Funding Information:
The authors gratefully acknowledge the contribution of the Scientific Grant Agency of the Slovak Republic (VEGA) under the grant 1/0988/16. MK gratefully recalls his communication with late Jaap Seidel and Ernie Shult, which was crucial for the shaping of his vision of the theory of two-graphs. He is also much obliged to all late and alive members of the former Moscow group for a fruitful communication. Special thanks go in this direction to Igor Farad?ev, the creator of the program part of COCO. Support of Christian Pech, Sven Reichard, as well as of Dennis Epple was very helpful and efficient. We are much obliged to Andries Brouwer, Peter Cameron and Gareth Jones for communications, which were supporting spirit of this project. We thank also Rosemary Bailey, Katie Brodhead, Willem Haemers, Josef Lauri, Mikhail Muzychuk, Andy Woldar and Yaokun Wu for helpful remarks. Personal attention of Don Thompson was crucial for the start of the project. The initial impulse in the creation of the paper came from Sasha Ivanov, J?n Karab??, Roman Nedela, Akihiro Munemasa, all our partners in the planning and running the event WL 2018. Finally, the authors are pleased to thank Jozef ?ir?? for his attention to this paper, as well as an anonymous referee for a very enthusiastic positive evaluation.
Funding Information:
Acknowledgements The authors gratefully acknowledge the contribution of the Scientific Grant Agency of the Slovak Republic (VEGA) under the grant 1/0988/16.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020/1/1

Y1 - 2020/1/1

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.

KW - Algebraic graph theory

KW - Antipodal graph

KW - Association scheme

KW - Block design

KW - COCO

KW - Coherent configuration

KW - Computer algebra

KW - Distance regular graph

KW - Dodecahedron

KW - Finite permutation group

KW - GAP

KW - Generalized quadrangle

KW - Icosahedron

KW - Inversive plane

KW - Paley graph

KW - Semi-icosahedron

KW - Strongly regular graph

KW - Two-graph

KW - Weisfeiler–Leman stabilization

UR - http://www.scopus.com/inward/record.url?scp=85079087749&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-32808-5_4

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

M3 - Conference contribution

AN - SCOPUS:85079087749

SN - 9783030328078

T3 - Springer Proceedings in Mathematics and Statistics

SP - 73

EP - 154

BT - Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016

A2 - Jones, Gareth A.

A2 - Ponomarenko, Ilia

A2 - Širán, Jozef

PB - Springer

T2 - International workshop on Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, WAGT 2016

Y2 - 3 October 2016 through 7 October 2016

ER -