Chromatic polynomial: различия между версиями
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'''Chromatic polynomial''' | '''Chromatic polynomial''' — [[хроматический полином графа]]. | ||
A '''chromatic polynomial''' <math>P_{G}(\lambda)</math> of a graph <math>G</math> is the number of good | A '''chromatic polynomial''' <math>\,P_{G}(\lambda)</math> of a [[graph, undirected graph, nonoriented graph|graph]] <math>\,G</math> is the number of good <math>\,\lambda</math>-[[coloring, colouring|colorings]] of <math>\,G</math> (<math>\lambda = 0, 1, \ldots</math>). | ||
<math>\lambda</math>-colorings of <math>G</math> (<math>\lambda = 0, 1, \ldots</math>). | This is a polynomial in <math>\,\lambda</math> (for a fixed <math>\,G</math>) and so, its | ||
This is a polynomial in <math>\lambda</math> (for a fixed <math>G</math>) and so, its | |||
definition can be extended to all real (or complex) values of | definition can be extended to all real (or complex) values of | ||
<math>\lambda</math>. Note that two <math>\lambda</math>-colorings differing in the | <math>\,\lambda</math>. Note that two <math>\,\lambda</math>-colorings differing in the | ||
labeling of colors are considered as different. | labeling of colors are considered as different. | ||
==Литература== | |||
* Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009. | |||
Текущая версия от 12:46, 18 апреля 2013
Chromatic polynomial — хроматический полином графа.
A chromatic polynomial [math]\displaystyle{ \,P_{G}(\lambda) }[/math] of a graph [math]\displaystyle{ \,G }[/math] is the number of good [math]\displaystyle{ \,\lambda }[/math]-colorings of [math]\displaystyle{ \,G }[/math] ([math]\displaystyle{ \lambda = 0, 1, \ldots }[/math]). This is a polynomial in [math]\displaystyle{ \,\lambda }[/math] (for a fixed [math]\displaystyle{ \,G }[/math]) and so, its definition can be extended to all real (or complex) values of [math]\displaystyle{ \,\lambda }[/math]. Note that two [math]\displaystyle{ \,\lambda }[/math]-colorings differing in the labeling of colors are considered as different.
Литература
- Евстигнеев В.А., Касьянов В.Н. Словарь по графам в информатике. — Новосибирск: Сибирское Научное Издательство, 2009.