2015/11/09 by Pablo Spiga · 3 citations
Mathematics · Engineering · #Finite Group Theory Research #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · doi:10.1112/blms/bdv071
Let Γ be a connected G-vertex-transitive graph, let v be a vertex of Γ and let G v Γ ( v ) be the permutation group induced by the action of the vertex-stabilizer G v on the neighbourhood Γ ( v ) . The graph Γ is said to be G-locally primitive if G v Γ ( v ) is primitive. Weiss conjectured in 1978 that there exists a function f : N → N such that, if Γ is a connected G-vertex-transitive locally primitive graph of valency d and v is a vertex of Γ with | G v | finite, then | G v | ⩽ f ( d ) . As an application of the Local C ( G , T ) Theorem, we prove this conjecture when G v Γ ( v ) contains an abelian regular subgroup. In fact, we show that the point-wise stabilizer in G of a ball of Γ of radius 4 is the identity subgroup.