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Zbl 0857.05061
Reid, Michael
On the connectivity of unit distance graphs. (English)
[J] Graphs Comb. 12, No.3, 295-303 (1996). ISSN 0911-0119; ISSN 1435-5914

Given a field $K\subseteq R$ and an integer $d>1$, the graph $G(K^d)$ is defined whose vertices are elements of $K^d$, with an edge between any two points at (Euclidean) distance 1. The author proves that $G(K^2)$ is not connected while $G(K^d)$ is connected for $d\ge5$; $G(K^4)$ is connected if and only if $G(K^3)$ is connected. Also necessary and sufficient conditions for the connectedness of $G(K^3)$ are given.
[Ján Plesník (Bratislava)]

MSC 2000:: *05C40 Connectivity
05C12 Distance in graphs

Keywords: unit distance graphs; connectedness

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