For a connected graph 
of graph diameter 
, the distance-
graph 
for 
, ..., 
is a graph with the same vertex
set and having edge set consisting of the pairs of
vertices that lie a distance 
apart. It is therefore the case that 
.
Distance graphs of interest (because they are distance-regular) include the distance-2 graphs of the Gosset graph, Hoffman-Singleton graph, and 24-Klein graph and the distance-3 graphs of the Heawood graph (quartic vertex-transitive graph Qt31) and 6-folded cube graph.
