Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583977 | Journal of Algebra | 2016 | 36 Pages |
Abstract
Let p be a prime and let LL be either the intransitive permutation group Cp×CpCp×Cp of degree 2p or the transitive permutation group CpwrC2 of degree 2p. Let Γ be a connected G-vertex-transitive and G-edge-transitive graph and let v be a vertex of Γ. We show that if the permutation group induced by the vertex-stabiliser GvGv on the neighbourhood Γ(v)Γ(v) is isomorphic to LL then either |V(Γ)|≥p|Gv|logp(|Gv|/2)|V(Γ)|≥p|Gv|logp(|Gv|/2), or |V(Γ)||V(Γ)| is bounded by a constant depending only on p, or Γ is a very-well understood graph. This generalises a few recent results.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Pablo Spiga, Gabriel Verret,