Enumerating Abelian Typical Cube-Free Fold Coverings of a Circulant Graph

• 来源期刊: 代数集刊（英文版）
• 关键词: graph covering enumeration voltage assignment circulant graph
• 年，卷（期）: 2020,（1）
• 页码范围: 137-148
• 页数: 12页
• 语种: 英文
• DOI: 10.1142/S1005386720000127

摘要

Enumerating the isomorphism or equivalence classes of several types of graph coverings is one of the central research topics in enumerative topological graph theory.A covering projection p from a Cayley graph Cay(Γ,X) onto another Cayley graph Cay(Q,Y) is called typical if the function p:F → Q on the vertex sets is a group epimorphism.A typical covering is called abelian (or circulant,respectively) if its covering graph is a Cayley graph on an abelian (or a cyclic,respectively) group.Recently,the equivalence classes of connected abelian typical prime-fold coverings of a circulant graph are enumerated.As a continuation of this work,we enumerate the equivalence classes of connected abelian typical cube-free fold coverings of a circulant graph.