On Cubic Graphs Admitting an Edge-Transitive Solvable Group

被引：0

作者：

Aleksander Malnič

Dragan Marušič

Primož Potočnik

机构：

[1] Univerza v Ljubljani,IMFM, Oddelek za matematiko

来源：

Journal of Algebraic Combinatorics | 2004年 / 20卷

关键词：

symmetric graph; edge transitive graph; cubic graph; trivalent graph; covering projection of graphs; solvable group of automorphisms;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Using covering graph techniques, a structural result about connected cubic simple graphs admitting an edge-transitive solvable group of automorphisms is proved. This implies, among other, that every such graph can be obtained from either the 3-dipole Dip3 or the complete graph K4, by a sequence of elementary-abelian covers. Another consequence of the main structural result is that the action of an arc-transitive solvable group on a connected cubic simple graph is at most 3-arc-transitive. As an application, a new infinite family of semisymmetric cubic graphs, arising as regular elementary abelian covering projections of K3,3, is constructed.

引用

页码：99 / 113

页数：14

共 18 条

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