Coadjoint pair: различия между версиями

'''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, 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

::::::<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}

=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