Vertex-Transitive Non-Cayley Graphs with Arbitrarily Large Vertex-Stabilizer
نویسندگان
چکیده
A construction is given for an infinite family {0n} of finite vertex-transitive non-Cayley graphs of fixed valency with the property that the order of the vertex-stabilizer in the smallest vertex-transitive group of automorphisms of 0n is a strictly increasing function of n. For each n the graph is 4-valent and arc-transitive, with automorphism group a symmetric group of large prime degree p> 22 +2. The construction uses Sierpinski’s gasket to produce generating permutations for the vertex-stabilizer (a large 2-group).
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