Distance graphs on R n with 1-norm

Jer-Jeong Chen () and Gerard J. Chang ()
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Jer-Jeong Chen: China University of Technology
Gerard J. Chang: National Taiwan University

Journal of Combinatorial Optimization, 2007, vol. 14, issue 2, No 16, 267-274

Abstract: Abstract Suppose S is a subset of a metric space X with metric d. For each subset D⊆{d(x,y):x,y∈S,x≠y}, the distance graph G(S,D) is the graph with vertex set S and edge set E(S,D)={xy:x,y∈S,d(x,y)∈D}. The current paper studies distance graphs on the n-space R 1 n with 1-norm. In particular, most attention is paid to the subset Z 1 n of all lattice points of R 1 n . The results obtained include the degrees of vertices, components, and chromatic numbers of these graphs.

Keywords: Metric space; Distance graph; 1-norm; Chromatic number; Degree; Component (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10878-007-9053-9

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