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:
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 -