## Abstract

A 2-distance *k*-coloring of a graph *G* is a mapping from *V* (*G*) to the set of colors {1,. . ., *k*} such that every two vertices at distance at most 2 receive distinct colors. The 2-distance chromatic number *χ*
_{2}(*G*) of *G* is then the smallest *k* for which *G* admits a 2-distance *k*-coloring. For any finite set of positive integers *D* = {*d*
_{1}, . . ., *d _{ℓ}*}, the integer distance graph

*G*=

*G*(

*D*) is the infinite graph defined by

*V*(

*G*) = ℤ and

*uv*∈

*E*(

*G*) if and only if |

*v*−

*u*| ∈

*D*. We study the 2-distance chromatic number of integer distance graphs for several types of sets

*D*. In each case, we provide exact values or upper bounds on this parameter and characterize those graphs

*G*(

*D*) with

*χ*2(

*G*(

*D*)) = ∆(

*G*(

*D*)) + 1.