Advances and Applications in Discrete Mathematics
Volume 2, Issue 2, Pages 103 - 115
(October 2008)
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ON THE DISTANCE CHROMATIC NUMBER OF HAMMING GRAPHS
Walter Klotz (Germany) and Elham Sharifiyazdi (Germany)
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of
a graph G
has
the same vertex set as G.
Distinct vertices in
are
adjacent, if their distance in G
is
at most d.
The distance chromatic number
of G
relative
to distance d
is
the chromatic number of
For positive integers q,
n the
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 d
and n,
we
show