On 1-arc-regular graphs

DOI10.1006/eujc.2002.0579zbMath1014.05033OpenAlexW2034271802MaRDI QIDQ1864592

Jie Wang, Ming-Yao Xu, Xin Gui Fang

Publication date: 18 March 2003

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/eujc.2002.0579

zbMATH Keywords

Cayley graphssolvable groupssimple groupstrivalent graphsvertex-transitive graphsedge-transitive graphsarc-transitive graphsarc-regular graphs

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (19)

Symmetric cubic graphs with non-solvable automorphism groups ⋮ Constructing one-regular graphs of valency 4\(k\) with non-cyclic vertex stabilizer ⋮ Edge-transitive regular metacyclic covers of the Petersen graph ⋮ Parametrization of Actions of the Automorphism Subgroup of a Cubic Tree onPL(F_p) ⋮ ON ARC-REGULAR FROBENIUS METACIRCULANTS ⋮ One-regular cubic graphs of order a small number times a prime or a prime square ⋮ There exist no arc-regular prime-valent graphs of order four times an odd square-free integer ⋮ One-regular graphs of square-free order of prime valency ⋮ An infinite family of cubic one-regular graphs with unsolvable automorphism groups. ⋮ Pentavalent symmetric graphs of order \(2pq\) ⋮ s-Arc-regular prime-valent Cayley graphs of square-free order ⋮ Symmetric cubic graphs with solvable automorphism groups ⋮ Pentavalent symmetric graphs of order 16p ⋮ On Finite 2-Path-Transitive Graphs ⋮ Pentavalent One-regular Graphs of Square-free Order ⋮ Infinitely many one-regular Cayley graphs on dihedral groups of any prescribed valency ⋮ Cubic vertex-transitive graphs of order 2pq ⋮ Cubic symmetric graphs of order twice an odd prime-power ⋮ Connected cubic \(s\)-arc-regular Cayley graphs of finite nonabelian simple groups

Cites Work

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• The maximal subgroups of the Chevalley groups \(G_ 2(q)\) with q odd, the Ree groups \(2G_ 2(q)\), and their automorphism groups
• On the full automorphism group of a graph
• Ree groups and Riemann surfaces
• Remarks on path-transitivity in finite graphs
• Vertex-transitive graphs
• The trivalent symmetric graphs of girth at most six
• A Family of Simple Groups Associated with the Simple Lie Algebra of Type (G 2 )
• An O'Nan-Scott Theorem for Finite Quasiprimitive Permutation Groups and an Application to 2-Arc Transitive Graphs
• Isomorphism problem for a class of point-symmetric structures
• Fintte two-arc transitive graphs admitting a suzuki simple group
• A One-Regular Graph of Degree Three

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