The
-dimensional
half cube is the graph whose vertices are the binary strings of length
,
with an even number of 1’s, and with two vertices adjacent if and only
if they differ in exactly two positions. It is also the 1-skeleton of an
-dimensional
polytope (called the
half cube polytope) whose cells are
-dimensional simplices
and
-dimensional
half cube polytopes.
We compute the automorphism groups of the half cube graphs by embedding their
vertices in
and realizing the automorphism groups as subgroups of
. As a
consequence, the automorphism group of a half cube graph coincides with its
automorphism group as a polytope.
Keywords
half cube, graph automorphism group, hypercube, graph
automorphism group
