A Construction for Vertex-Transitive Graphs
A Construction for Vertex-Transitive Graphs
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DOI：
10.4153/cjm-1982-020-8
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发表时间：
1982-04
期刊：
影响因子：
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通讯作者：
B. Alspach;T. Parsons
中科院分区：
文献类型：
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作者：
B. Alspach;T. Parsons
构造有趣的点传递图族的一个有用的一般策略是开始于某个传递置换群族，并为该群族中的每个群Γ构造所有图G，其顶点集是Γ的轨道V，且对该图G，Γ ∈ Aut（G），其中Aut（G）表示G的自同构群。例如，如果我们考虑由长度为n的圈（0，1.n-1）生成的循环群族，则相应的图是n-顶点循环图。本文考虑由m个长度为n的不相交圈的“旋转”ρ和“扭曲平移”t生成的mn次可迁置换群，使得对α，τρτ-l = ρα.
A useful general strategy for the construction of interesting families of vertex-transitive graphs is to begin with some family of transitive permutation groups and to construct for each group Γ in the family all graphs G whose vertex–set is the orbit V of Γ and for which Γ ≦ Aut (G), where Aut (G) denotes the automorphism group of G. For example, if we consider the family of cyclic groups 〈(0 1 … n – 1)〉 generated by cycles (0, 1 … n – 1) of length n, then the corresponding graphs are the n-vertex circulant graphs. In this paper we consider transitive permutation groups of degree mn generated by a “rotation” ρ which is a product of m disjoint cycles of length n and by a “twisted translation” t; such that τρτ–l = ρα for some α.