论文标题

基础图 - 连接图:解剖和施工

Base Graph -- Connection Graph: Dissection and Construction

论文作者

Verret, Gabriel, Potočnik, Primož, Wilson, Steve

论文摘要

本文提出了一种现象,该现象有时会发生在四分之二的局部飞镖传输图中,称为基本图 - 连接图解剖。在此解剖中,每个白色顶点分为价2的两个顶点,因此结果的连接成分是同构的。鉴于基本图的细分是每个组件的同构,而连接图(描述了组件重叠的方式),在某些情况下,我们可以提供可以使图具有如此分解的图形的结构。本文研究了一般现象以及连接图的特殊情况不超过一个边缘。

This paper presents a phenomenon which sometimes occurs in tetravalent bipartite locally dart-transitive graphs, called a Base Graph -- Connection Graph dissection. In this dissection, each white vertex is split into two vertices of valence 2 so that the connected components of the result are isomorphic. Given the Base Graph whose subdivision is isomorphic to each component, and the Connection Graph, which describes how the components overlap, we can, in some cases, provide a construction which can make a graph having such a decomposition. This paper investigates the general phenomenon as well as the special cases in which the connection graph has no more than one edge.

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