КФУ. Карточка публикации. Explicit formulas for chromatic polynomials of some series-parallel graphs/

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EXPLICIT FORMULAS FOR CHROMATIC POLYNOMIALS OF SOME SERIES-PARALLEL GRAPHS/

Форма представления

Статьи в российских журналах и сборниках

Год публикации

2018

Язык

английский

Авторы, сотрудники КФУ

Лернер Эдуард Юльевич, автор

Мухамеджанова Софья Альфисовна, автор

Библиографическое описание на языке оригинала

Lerner E.Yu. Explicit formulas for chromatic polynomials of some series-parallel graphs/ Lerner E.Yu., Mukhamedjanova S.A. // Ученые записки Казанского университета. Серия Физ.-мат. Науки, 2018. Том 160, Кн. 2, стр. 339-349

Аннотация

The main goal of our paper is to present explicit formulas for chromatic polynomials of some planar series-parallel graphs (sp-graphs). The necklace-graph considered in this paper is the simplest non-trivial sp-graph. We have provided the explicit formula for calculating the chromatic polynomial of common sp-graphs. In addition, we have presented the explicit formulas for calculating chromatic polynomials of the ring of the necklace graph and the necklace of the necklace graph. Chromatic polynomials of the necklace graph and the ring of the necklace graph have been initially obtained by transition to the dual graph and the subsequent using of the flow polynomial. We have also used the technique of finite Fourier transformations. The use of the partition function of the Potts model is a more general way to evaluate chromatic polynomials. In this method, we have used and modified the parallel- and series-reduction identities that were introduced by A. Sokal.

Ключевые слова

chromatical polynomial, partition function of Potts model, Tutte polynomial, Fourier transform, series-parallel graph, necklace graph

Название журнала

Ученые записки Казанского государственного университета Серия: Физико-математические науки

URL

https://kpfu.ru/2018-tom-160-kniga-2_354394.html

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https://repository.kpfu.ru/?p_id=234424

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Лернер Эдуард Юльевич	ru_RU
dc.contributor.author	Мухамеджанова Софья Альфисовна	ru_RU
dc.date.accessioned	2018-01-01T00:00:00Z	ru_RU
dc.date.available	2018-01-01T00:00:00Z	ru_RU
dc.date.issued	2018	ru_RU
dc.identifier.citation	Lerner E.Yu. Explicit formulas for chromatic polynomials of some series-parallel graphs/ Lerner E.Yu., Mukhamedjanova S.A. // Ученые записки Казанского университета. Серия Физ.-мат. Науки, 2018. Том 160, Кн. 2, стр. 339-349	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=234424	ru_RU
dc.description.abstract	Ученые записки Казанского государственного университета Серия: Физико-математические науки	ru_RU
dc.description.abstract	The main goal of our paper is to present explicit formulas for chromatic polynomials of some planar series-parallel graphs (sp-graphs). The necklace-graph considered in this paper is the simplest non-trivial sp-graph. We have provided the explicit formula for calculating the chromatic polynomial of common sp-graphs. In addition, we have presented the explicit formulas for calculating chromatic polynomials of the ring of the necklace graph and the necklace of the necklace graph. Chromatic polynomials of the necklace graph and the ring of the necklace graph have been initially obtained by transition to the dual graph and the subsequent using of the flow polynomial. We have also used the technique of finite Fourier transformations. The use of the partition function of the Potts model is a more general way to evaluate chromatic polynomials. In this method, we have used and modified the parallel- and series-reduction identities that were introduced by A. Sokal.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	chromatical polynomial	ru_RU
dc.subject	partition function of Potts model	ru_RU
dc.subject	Tutte polynomial	ru_RU
dc.subject	Fourier transform	ru_RU
dc.subject	series-parallel graph	ru_RU
dc.subject	necklace graph	ru_RU
dc.title	Explicit formulas for chromatic polynomials of some series-parallel graphs/	ru_RU
dc.type	Статьи в российских журналах и сборниках	ru_RU