In the mathematical discipline of graph theory, the medial graph of plane graph G is another graph M(G) that represents the adjacencies between edges in the faces of G. Medial graphs were introduced in 1922 by Ernst Steinitz to study combinatorial properties of convex polyhedra, although the inverse construction was already used by Peter Tait in 1877 in his foundational study of knots and links.
In the mathematical discipline of graph theory, the medial graph of plane graph G is another graph M(G) that represents the adjacencies between edges in the faces of G. Medial graphs were introduced in 1922 by Ernst Steinitz to study combinatorial properties of convex polyhedra, although the inverse construction was already used by Peter Tait in 1877 in his foundational study of knots and links.
case
in
In
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
mathematical
mathematical
ADJ
JJ
obl
Number=Sing
discipline
discipline
NOUN
NN
case
of
of
ADP
IN
compound
Number=Sing
graph
graph
NOUN
NN
nmod
Number=Sing
theory
theory
NOUN
NN
punct
,
,
PUNCT
,
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
medial
medial
ADJ
JJ
nsubj
Number=Sing
graph
graph
NOUN
NN
case
of
of
ADP
IN
compound
Number=Sing
plane
plane
NOUN
NN
nmod
Number=Sing
graph
graph
NOUN
NN
appos
Number=Sing
G
G
PROPN
NNP
cop
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
be
is
AUX
VBZ
det
another
another
DET
DT
compound
Number=Sing
graph
graph
NOUN
NN
root
Number=Sing
M
M
NOUN
NN
punct
(
(
PUNCT
-LRB-
appos
Number=Sing
G
G
PROPN
NNP
punct
)
)
PUNCT
-RRB-
nsubj
PronType=Rel
that
that
PRON
WDT
acl:relcl
Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin
represent
represents
VERB
VBZ
det
Definite=Def|PronType=Art
the
the
DET
DT
obj
Number=Plur
adjacency
adjacencies
NOUN
NNS
case
between
between
ADP
IN
nmod
Number=Plur
edge
edges
NOUN
NNS
case
in
in
ADP
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
nmod
Number=Plur
face
faces
NOUN
NNS
case
of
of
ADP
IN
compound
Number=Sing
G.
G.
PROPN
NNP
flat
Number=Sing
Medial
Medial
PROPN
NNP
nmod
Number=Plur
graph
graphs
NOUN
NNS
aux:pass
Mood=Ind|Number=Plur|Person=3|Tense=Past|VerbForm=Fin
be
were
AUX
VBD
acl
Tense=Past|VerbForm=Part|Voice=Pass
introduce
introduced
VERB
VBN
case
in
in
ADP
IN
obl
NumForm=Digit|NumType=Card
1922
1922
NUM
CD
case
by
by
ADP
IN
obl:agent
Number=Sing
Ernst
Ernst
PROPN
NNP
flat
Number=Sing
Steinitz
Steinitz
PROPN
NNP
mark
to
to
PART
TO
advcl
VerbForm=Inf
study
study
VERB
VB
amod
Degree=Pos
combinatorial
combinatorial
ADJ
JJ
obj
Number=Plur
property
properties
NOUN
NNS
case
of
of
ADP
IN
compound
Number=Sing
convex
convex
NOUN
NN
nmod
Number=Sing
polyhedra
polyhedra
NOUN
NN
punct
,
,
PUNCT
,
mark
although
although
SCONJ
IN
det
Definite=Def|PronType=Art
the
the
DET
DT
amod
Degree=Pos
inverse
inverse
ADJ
JJ
nsubj:pass
Number=Sing
construction
construction
NOUN
NN
aux:pass
Mood=Ind|Number=Sing|Person=3|Tense=Past|VerbForm=Fin
be
was
AUX
VBD
advmod
already
already
ADV
RB
advcl
Tense=Past|VerbForm=Part|Voice=Pass
use
used
VERB
VBN
case
by
by
ADP
IN
obl:agent
Number=Sing
Peter
Peter
PROPN
NNP
flat
Number=Sing
Tait
Tait
PROPN
NNP
case
in
in
ADP
IN
obl
NumForm=Digit|NumType=Card
1877
1877
NUM
CD
case
in
in
ADP
IN
nmod:poss
Case=Gen|Gender=Masc|Number=Sing|Person=3|Poss=Yes|PronType=Prs
his
his
PRON
PRP$
amod
Degree=Pos
foundational
foundational
ADJ
JJ
obl
Number=Sing
study
study
NOUN
NN
case
of
of
ADP
IN
nmod
Number=Plur
knot
knots
NOUN
NNS
cc
and
and
CCONJ
CC
conj
Number=Plur
link
links
NOUN
NNS
punct
.
.
PUNCT
.