Geodesic
Edge colorings and total colorings of integer distance graphs
Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 149-158

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An integer distance graph is a graph G(D) with the set Z of integers as vertex set and two vertices u,v ∈ Z are adjacent if and only if |u-v| ∈ D where the distance set D is a subset of the positive integers N. In this note we determine the chromatic index, the choice index, the total chromatic number and the total choice number of all integer distance graphs, and the choice number of special integer distance graphs.
Keywords: integer distance graph, chromatic number, choice number, chromatic index, choice index, total chromatic number, total choice number 
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Kemnitz, Arnfried; Marangio, Massimiliano. Edge colorings and total colorings of integer distance graphs. Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 149-158. http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a11/