Last Updated
：2025/12/07
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.
Japanese Meaning
幾何学において、ケラーの予想に関連するグラフの族の一つ。具体的には、次元 n のケラーグラフは 4ⁿ 個の頂点から構成され、各頂点は n 個の値 (m₁, …, mₙ) を持ち、各 m は 0, 1, 2, 3 のいずれかの値をとる。また、2 つの頂点が辺で結ばれる条件は、少なくとも2つの座標において値が異なり、そのうち少なくとも1つの座標で値の差がちょうど2である場合に成立する。
Sense（1）
(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.
（ plural ）
Quizzes for review
(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.
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See correct answer
Keller graph
By examining the adjacency rules for a Keller graph, researchers can systematically test configurations relevant to Keller's conjecture in dimension n.
See correct answer
By examining the adjacency rules for a Keller graph, researchers can systematically test configurations relevant to Keller's conjecture in dimension n.
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