Distance graphs on R-n supercript stop with 1-norm
Suppose S is a subset of a metric space X with metric d. For each subset D subset of {d(x,y):x,y epsilon S,x not equal y}, the distance graph G(S,D) is the graph with vertex set S and edge set E(S,D)={xy:x,y epsilon S,d(x,y) epsilon 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.
distance graph 1-norm metric space degree component chromatic number