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Unit-distance graphs in rational n-spaces

✍ Scribed by Kiran B. Chilakamarri

Publisher: Elsevier Science
Year: 1988
Tongue: English
Weight: 576 KB
Volume: 69
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90049-0

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✦ Synopsis

Let Un be the infinite graph with n-dimensional rational space Q" as vertex set and two vertices joined by an edge if and only if the distance between them is exactly 1. The connectedness and clique numbers of the graphs U' are discwed. z * .

In this section we shall first prove that U1, U2, U3, and U4 are all disconnected and prove that U, is connected for n a 5.

. There is no path in U4 connecting the origin (0, 0, 0,O) to (g,

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