KFU. Card publication. Explicit formulas for chromatic polynomials of some series-parallel graphs

KAZAN
FEDERAL UNIVERSITY

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EXPLICIT FORMULAS FOR CHROMATIC POLYNOMIALS OF SOME SERIES-PARALLEL GRAPHS

Form of presentation

Articles in Russian journals and collections

Year of publication

2018

Язык

английский

Authors, employees of KFU

Lerner Eduard Yulevich, author

Bibliographic description in the original language

Lerner E.Yu. Explicit formulas for chromatic polynomials of some series-parallel graphs/ Lerner E.Yu., Mukhamedjanova S.A. // Uchenye zapiski Kazanskogo universiteta. Seriya Fiz.-mat. Nauki, 2018. Tom 160, Kn. 2, str. 339-349

Annotation

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.

Keywords

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

The name of the journal

Ученые записки Казанского государственного университета Серия: Физико-математические науки

URL

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

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=190494&p_lang=2

Resource files

File name	Size (MB)	Format
Lerner_Muhamedjanova.pdf	3,74	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Lerner Eduard Yulevich	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/eng/?p_id=190494&p_lang=2	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	Articles in Russian journals and collections	ru_RU