✦ LIBER ✦

Connectivity of distance graphs

✍ Scribed by J.D. Currie

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 243 KB
Volume: 103
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90042-e

No coin nor oath required. For personal study only.

✦ Synopsis

Currie, J.D., Connectivity of distance graphs, Discrete Mathematics 103 (1992) 91-94.

The author shows the following: Let K 2 Q be a H-module. Let G be a graph with vertex set V, a K-space. Suppose that edges of G are preserved under translations in V. Then if G has more than one connected component, it has infinitely many. In particular, suppose K is a field, K E Iw. For a given n E N, consider the unit distance graph G whose vertices are the points of K", with an edge between any two points at unit distance. If G is not connected, then G must have infinitely many components.

This answers a question of Zaks.

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