Square-free non-Cayley numbers. On vertex-transitive non-Cayley graphs of square-free order.

DOI10.1007/s10623-004-4859-2zbMath1075.20002OpenAlexW2019940421MaRDI QIDQ1766111

Cai Heng Li, Seress, Ákos

Publication date: 28 February 2005

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-004-4859-2

zbMATH Keywords

primitive permutation groupsCayley graphsBurnside groupsregular subgroupsvertex-transitive graphsnon-Cayley numbers

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Primitive groups (20B15)

Related Items (13)

Cubic vertex-transitive non-Cayley graphs of order \(12p\) ⋮ Super cyclically edge-connected vertex-transitive graphs of girth at least 5 ⋮ Tetravalent vertex-transitive graphs of order twice a prime square ⋮ Cayley numbers with arbitrarily many distinct prime factors ⋮ Enumerating graphs via even/odd dichotomy ⋮ On cubic symmetric non-Cayley graphs with solvable automorphism groups ⋮ The symmetry property of (n,k)‐arrangement graph ⋮ THE TWO-ARC-TRANSITIVE GRAPHS OF SQUARE-FREE ORDER ADMITTING ALTERNATING OR SYMMETRIC GROUPS ⋮ Existence of non-Cayley Haar graphs ⋮ Symmetric cubic graphs with solvable automorphism groups ⋮ Why do mathematicians need different ways of presenting mathematical objects? The case of Cayley graphs ⋮ Regular subgroups of primitive permutation groups ⋮ On cubic non-Cayley vertex-transitive graphs

Uses Software

• GAP

Cites Work

• Non-Cayley vertex-transitive graphs of order twice the product of two odd primes
• Vertex-primitive graphs of order a product of two distinct primes
• On vertex-transitive, non-Cayley graphs of order \(pqr\)
• On finite near-fields
• On non-Cayley vertex-transitive graphs of order a product of three primes
• Transitivity of finite permutation groups on unordered sets
• \(k\)-homogeneous groups
• Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I
• Characterizing vertex-transitivepq-graphs with an imprimitive automorphism subgroup
• Vertex primitive graphs of order containing a large prime factor^*
• THE PRIMITIVE PERMUTATION GROUPS OF SQUAREFREE DEGREE
• The Finite Primitive Permutation Groups Containing an Abelian Regular Subgroup
• Vertex-primitive groups and graphs of order twice the product of two distinct odd primes
• Vertex-transitive graphs that are not Cayley graphs. II

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