| Форма представления | Статьи в российских журналах и сборниках |
| Год публикации | 2018 |
| Язык | английский |
|
Лернер Эдуард Юльевич, 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 |
| Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку |
https://repository.kpfu.ru/?p_id=190494 |
| Файлы ресурса | |
|
|
Полная запись метаданных  |
| Поле DC |
Значение |
Язык |
| dc.contributor.author |
Лернер Эдуард Юльевич |
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=190494 |
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 |
|
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