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Keller graph
noun
(geometry)
Any
of
a
certain
family
of
graphs
related
to
Keller's
conjecture,
such
that
the
vertices
of
the
Keller
graph
of
dimension
n
are
the
4ⁿ
elements
(m₁,...,mₙ)
where
each
m
is
0,
1,
2,
or
3,
and
two
vertices
are
joined
by
an
edge
if
they
differ
in
at
least
two
coordinates
and
differ
by
exactly
two
in
at
least
one
coordinate.
crown graph
noun
cubic graph
planar graph
noun
medial graph
noun
(graph
theory)
A
graph
derived
from
a
given
plane
graph
such
that
this
derived
graph
has
a
vertex
corresponding
to
each
edge
of
the
given
graph,
and
such
that
for
every
“angle”
(consecutive
trio
of
edge,
vertex,
edge)
along
the
border
of
a
face
of
the
given
graph
there
is
a
corresponding
edge
which
connects
the
vertices
corresponding
to
the
two
edges
that
are
part
of
that
“angle”.
dual graph
noun
(graph
theory)
A
graph
derived
from
some
plane
graph
in
such
a
way
that
the
derived
graph
has
a
vertex
corresponding
to
each
face
of
the
given
graph,
an
edge
corresponding
to
each
edge
of
the
given
graph
that
is
shared
by
a
pair
of
distinct
faces,
and
a
self-loop
for
each
edge
of
the
given
graph
that
is
a
border
of
the
same
face
on
both
of
its
sides.
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