Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers

DOI10.1016/j.jctb.2020.12.001zbMath1458.05266arXiv1908.09361OpenAlexW3112469262MaRDI QIDQ2222047

Binzhou Xia

Publication date: 3 February 2021

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.09361

zbMATH Keywords

half-arc-transitivetetravalent

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graph theory (05C99) Group actions on combinatorial structures (05E18)

Related Items (4)

Finite 3-connected-set-homogeneous locally \(2\mathbf{K}_n\) graphs and \(s\)-arc-transitive graphs ⋮ Resolution of a conjecture about linking ring structures ⋮ Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers ⋮ Constructing infinitely many half-arc-transitive covers of tetravalent graphs

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Constructing half-arc-transitive graphs of valency four with prescribed vertex stabilizers
• \(p\)-adic Hurwitz groups
• Smallest tetravalent half-arc-transitive graphs with the vertex-stabiliser isomorphic to the dihedral group of order 8
• On cubic \(s\)-arc transitive Cayley graphs of finite simple groups
• A note on the automorphism groups of cubic Cayley graphs of finite simple groups
• Symmetry properties of Cayley graphs of small valencies on the alternating group \(A_5\)
• 5-arc transitive cubic Cayley graphs on finite simple groups
• The automorphisms of bi-Cayley graphs
• On the order of vertex-stabilisers in vertex-transitive graphs with local group \(\mathrm{C}_p \times \mathrm{C}_p\) or \(\mathrm{C}_p\, \mathrm{wr}\, \mathrm{C}_2\)
• Finite edge-transitive oriented graphs of valency four: a global approach
• A classification of tightly attached half-arc-transitive graphs of valency 4
• Subgroups of prime power index in a simple group
• On the full automorphism group of a graph
• Maps and half-transitive graphs of valency 4
• On the minimal degree of a primitive permutation group
• Half-transitive group actions on finite graphs of valency 4
• Tetravalent graphs admitting half-transitive group actions: Alternating cycles
• Constructing 4-valent \(\frac 12\)-transitive graphs with a nonsolvable automorphism group
• On 4-valent symmetric graphs
• On cubic Cayley graphs of finite simple groups
• The Magma algebra system. I: The user language
• Recent developments in half-transitive graphs
• A tetravalent half-arc-transitive graph with non-abelian vertex stabilizer
• Half-transitivity of some metacirculants
• The graphical regular representations of finite metacyclic \(p\)-groups
• An infinite family of cubic nonnormal Cayley graphs on nonabelian simple groups
• New structural results on tetravalent half-arc-transitive graphs
• On certain edge-transitive bicirculants
• Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5
• The automorphism groups of some cubic Cayley graphs
• On edge-transitive Cayley graphs of valency four
• Hexavalent half-arc-transitive graphs of order \(9 p\)
• Simple group actions on arc-transitive graphs with prescribed transitive local action
• Finite edge-transitive oriented graphs of valency four with cyclic normal quotients
• Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers
• Constructing infinitely many half-arc-transitive covers of tetravalent graphs
• Tetravalent half-arc-transitive graphs of order \(p^5\)
• The classification of half-arc-transitive generalizations of Bouwer graphs
• On the radius and the attachment number of tetravalent half-arc-transitive graphs
• Cayley digraphs and graphs
• Quartic half-arc-transitive graphs with large vertex stabilizers
• On the point stabilizers of transitive groups with non-self-paired suborbits of length 2
• Tetravalent half-edge-transitive graphs and non-normal Cayley graphs
• Vertex-quasiprimitive 2-arc-transitive digraphs
• An O'Nan-Scott Theorem for Finite Quasiprimitive Permutation Groups and an Application to 2-Arc Transitive Graphs
• [https://portal.mardi4nfdi.de/wiki/Publication:4344215 A �-transitive graph of valency 4 with a nonsolvable group of automorphisms]
• On the Automorphism Groups of Cayley Graphs of Finite Simple Groups
• Half-transitive graphs of valency 4 with prescribed attachment numbers
• Cubic graphical regular representations of finite non-abelian simple groups
• Automorphism Groups of Bouwer Graphs
• Lifting a prescribed group of automorphisms of graphs
• A normal quotient analysis for some families of oriented four-valent graphs
• Some recent discoveries about half-arc-transitive graphs
• Vertex and Edge Transitive, but not 1-Transitive, Graphs
• Half-arc-transitive graphs of arbitrary even valency greater than 2

This page was built for publication: Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers