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- Title
Heptavalent Symmetric Graphs with Certain Conditions.
- Authors
Du, Jiali; Feng, Yanquan; Liu, Yuqin
- Abstract
A graph Γ is said to be symmetric if its automorphism group Aut (Γ) acts transitively on the arc set of Γ. We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group G of automorphisms, then either G is normal in Aut (Γ) , or Aut (Γ) contains a non-abelian simple normal subgroup T such that G ≤ T and (G , T) is explicitly given as one of 11 possible exceptional pairs of non-abelian simple groups. If G is arc-transitive, then G is always normal in Aut (Γ) , and if G is regular on the vertices of Γ , then the number of possible exceptional pairs (G , T) is reduced to 5.
- Subjects
MULTIPLY transitive groups; AUTOMORPHISM groups; AUTOMORPHISMS; SOLVABLE groups; CAYLEY graphs; NONABELIAN groups
- Publication
Algebra Colloquium, 2021, Vol 28, Issue 2, p243
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386721000195