The term "distance graph" refers to a graph constructed on a given vertex set where edges exist when two vertices are at some fixed distance (or set of allowed distances) from each other. A number of types of distances are commonly considered, including graph distance (giving a graph distance graph) and Euclidean distance (when the embedding of the vertex set is given, giving a Euclidean distance graph). A distance graph whose edges are determined based on vertices being a particular distance k apart is known as a distance-k graph.
