Tetravalent arc-transitive graphs with unbounded vertex-stabilisers

2010/10/13 by Primož Potočnik, Primoz Potocnik, Potocnik, Primoz +4
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Rings, Modules, and Algebras #math.CO

paper · pdf · doi:10.48550/arxiv.1010.2549

9 pages

arxiv created 2010/10/13 · arxiv updated 2010/10/14

Abstract

It has long been known that there exist finite connected tetravalent arc-transitive graphs with arbitrarily large vertex-stabilisers. However, beside a well known family of exceptional graphs, related to the lexicographic product of a cycle with an edgeless graph on two vertices, only a few such infinite families of graphs are known. In this paper, we present two more families of tetravalent arc-transitive graphs with large vertex-stabilisers, each significant for its own reason.

Related

• On tetravalent half-arc-transitive graphs
• Constructing infinitely many half-arc-transitive covers of tetravalent graphs
• Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers
• Vertex-transitive graphs and their arc-types
• Smallest tetravalent half-arc-transitive graphs with the vertex-stabiliser isomorphic to the dihedral group of order 8