On the connectivity of unit distance graphs
type: Item
instance of: scholarly article
title: On the connectivity of unit distance graphs
zbMATH Open document ID: 0857.05061
DOI: 10.1007/BF01858462
author: Yanyan Li
published in: Graphs and Combinatorics
publication date: 1997-03-06T00:00:00Z
review text: 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 \(d\geq5\); \(G(K^4)\) 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.
reviewed by: Ján Plesník
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 934041
zbMATH Keywords: unit distance graphs
zbMATH Keywords: connectedness
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01858462
OpenAlex ID: W1974176979
description: scientific article; zbMATH DE number 934041