A census of semisymmetric cubic graphs on up to 768 vertices
A census of semisymmetric cubic graphs on up to 768 vertices
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DOI：
10.1007/s10801-006-7397-3
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发表时间：
2006-05
影响因子：
0.8
通讯作者：
M. Conder;A. Malnic;D. Marušič;P. Potocnik
中科院分区：
文献类型：
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作者：
M. Conder;A. Malnic;D. Marušič;P. Potocnik
给出了阶数高达 768 的所有半对称（边但非顶点传递）连接的有限三次图的列表。该列表是由作者使用索引 (3,3) 的有限本原汞齐的 Goldschmidt 分类以及用于在有限呈现群中查找最多给定索引的所有正常子群的计算机算法确定的。该列表包括一些以前未被发现的图表。对于列表中的每个图，都提供了大量信息，包括其周长和直径、其自同构群的阶数、自同构的最小边传递群的阶数和结构、其 Goldschmidt 类型、稳定器分区以及有关其商和覆盖的其他详细信息。还给出了所有已知的半对称立方图的无限族的摘要，以及它们的构造的明确规则，并且用这些来标识列表的成员。详细研究了那些以 K1,3 作为正常商的图的特殊情况。
A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms, its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of the list are identified with these. The special case of those graphs havingK1,3as a normal quotient is investigated in detail.