Kazan (Volga region) Federal University, KFU
KAZAN
FEDERAL UNIVERSITY
 
EXPLICIT FORMULAS FOR CHROMATIC POLYNOMIALS OF SOME SERIES-PARALLEL GRAPHS/
Form of presentationArticles in Russian journals and collections
Year of publication2018
Языканглийский
  • Lerner Eduard Yulevich, author
  • Mukhamedzhanova Sofya Alfisovna, 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=234424&p_lang=2

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