Abstract: The
distance power of
a graph Ghas
the same vertex set as G.
Distinct vertices in are
adjacent, if their distance in Gis
at most d.
The distance chromatic number of Grelative
to distance dis
the chromatic number of For positive integers q,
nthe
Hamming graph has
as its vertex set the n-fold
Cartesian product Vertices
in are
adjacent, if they differ in exactly one coordinate. We derive explicit formulas
for the clique number and we determine some exact values of For fixed dand n,
we
show
Keywords and phrases: Hamming graph, distance power, chromatic number.
