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Coadjoint pair: различия между версиями

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'''Coadjoint pair''' --- сопряженная пара.  
'''Coadjoint pair''' — ''[[сопряженная пара]].''


A pair of operators <math>(A,P)</math> is a '''coadjoint pair''' if <math>A</math> is an ''adjacency operator'' <math>A(G)</math> for a graph <math>G</math> and <math>P = \sum_{v \in V(G)}
A pair of operators <math>\,(A,P)</math> is a '''coadjoint pair''' if <math>\,A</math> is an ''[[adjacency operator]]'' <math>\,A(G)</math> for a [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> and <math>P = \sum_{v \in V(G)} \varphi(v) \otimes v</math> is a permutation on <math>\,V(G)</math> satisfying
\varphi(v) \otimes v</math> is a permutation on <math>V(G)</math> satisfying


<math>A(G)^{\ast} = P^{\ast}A(G)P.</math>
::::::<math>A(G)^{\ast} = P^{\ast}A(G)P.</math>


Moreover, the bijection <math>\varphi</math> on <math>V(G)</math> satisfies <math>\varphi^{2}
Moreover, the bijection <math>\varphi</math> on <math>\,V(G)</math> satisfies <math>\varphi^{2}
=1</math>, or <math>P^{2} = 1</math>. In this case, <math>P</math> is called a '''transposition symmetry'''. Like this case, if a graph <math>G</math> has a '''coadjoint pair''' <math>(A,S)</math>
=1</math>, or <math>\,P^{2} = 1</math>. In this case, <math>\,P</math> is called a '''transposition symmetry'''. Like this case, if a graph <math>\,G</math> has a '''coadjoint pair''' <math>\,(A,S)</math> such that <math>\,S</math> is a transposition symmetry, then <math>\,G</math> is called '''strongly coadjoint'''. Needless to say, undirected graphs are all
such that <math>S</math> is a transposition symmetry, then <math>G</math> is called '''strongly coadjoint'''. Needless to say, undirected graphs are all
strongly coadjoint and strongly coadjoint graphs are all coadjoint.
strongly coadjoint and strongly coadjoint graphs are all coadjoint.
==Литература==
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.