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  2. Turkish Journal of Science
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  4. Cilt 5, Sayı 3
Yıl 2020, Cilt 5 , Sayı 3, Sayfalar 262 - 267 2020-12-30

The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group

Bünyamin ŞAHİN [1] , Abdulgani ŞAHİN [2]

Öz

The Grigorchuk group was first introduced by R. Grigorchuk in 1980. Also the Basilica group was introduced in 2002 by R. Grigorchuk and A. Zuk. In the following years, it was shown that these groups have deep connections with profinite group theory and complex dynamics. These groups have been proven to provide the self-similarity property, reflecting the fractalness of some limit objects associated with them. The Schreier graph codifies the intangible structure of a group. It establishes an equivalence relationship created by cosets. The Schreier graphs of the Grigorchuck group and the Basilica group are a combination of cycles arranged in a tree-like form due to the recursive expression of the generators of these groups. In this work, we study the Hosoya polynomial of these graphs and try to characterize them.

Anahtar Kelimeler

Basilica group, Grigorchuk group, Hosoya polynomial, Schreier graph

Kaynakça

  • [1] Bartholdi L, Grigorchuk R, Nekrashevych V. From fractal groups to fractal sets, in: “Fractals in Graz” (P. Grabner and W. Woess editors). Trends in Mathematics. Birkauser Verlag, Basel, 2003, 25 – 118.
  • [2] Bartholdi L, Virag B. Amenability via random walks. Duke Math Journal. 130(1), 2005, 39 – 56.
  • [3] Ceccherini-Silberstein T, Donno A, Iacono D. The Tutte polynomial of the Schreier graphs for the Grigorchuck group and the Basilica group. Ischia Group Theory. 2010, 2011, 45 – 68.
  • [4] Deutsch E, Klavzar S. Computing Hosoya polynomials of graphs from primary subgraphs. MATCH Communications in Mathematical and in Computer Chemistry. 70(2), 2013, 627 – 644.
  • [5] Deutsch E, Klavzar S. The Hosoya polynomial of distance-regular graphs. Discrete Applied Mathematics. 178, 2014, 153 – 156.
  • [6] Grigorchuk R, Zuk A. On a torsion-free weakly branch group defined by a three-state automaton. International J. Algebra Comput. 12(1), 2002, 223 – 246.
  • [7] Grigorchuk R. Solved and unsolved problems around one group, ınfinite groups: geometric, combinatorial and dynamical aspects. Progr. Math. 248, Birkhauser, Basel, 2005, 117 – 218.
  • [8] Hosoya H. On some counting polynomials in chemistry. Discrete Applied Mathematics. 19(1–3), 1988, 239 – 257.
  • [9] Nekrashevych V. Self-Similar Groups. Mathematical Surveys and Monographs, 117. American Mathematical Society, Providence, RI, 2005.
  • [10] Şahin A, Şahin B. Hosoya polynomial of graphs belonging to twist knots. Turk. J. Math. Comput. Sci. 10, 2018, 38 – 42.

Ayrıntılar

Birincil Dil en
Konular Fen
Bölüm Volume V Issue III 2020
Yazarlar

Orcid: 0000-0003-1094-5481
Yazar: Bünyamin ŞAHİN
Kurum: SELÇUK ÜNİVERSİTESİ
Ülke: Turkey

Orcid: 0000-0002-9446-7431
Yazar: Abdulgani ŞAHİN (Sorumlu Yazar)
Kurum: Ağrı İbrahim Çeçen Üniversitesi
Ülke: Turkey
Tarihler

Yayımlanma Tarihi : 30 Aralık 2020

Kaynak Göster

Bibtex @araştırma makalesi { tjos846400, journal = {Turkish Journal of Science}, issn = {2587-0971}, eissn = {2587-0971}, address = {KED YAYINCILIK LTD. ŞTİ. Ağrı}, publisher = {Ahmet Ocak AKDEMİR}, year = {2020}, volume = {5}, pages = {262 - 267}, doi = {}, title = {The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group}, key = {cite}, author = {Şahin, Bünyamin and Şahin, Abdulgani} }
APA Şahin, B , Şahin, A . (2020). The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group . Turkish Journal of Science , 5 (3) , 262-267 . Retrieved from https://dergipark.org.tr/tr/pub/tjos/issue/59057/846400
MLA Şahin, B , Şahin, A . "The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group" . Turkish Journal of Science 5 (2020 ): 262-267 <https://dergipark.org.tr/tr/pub/tjos/issue/59057/846400>
Chicago Şahin, B , Şahin, A . "The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group". Turkish Journal of Science 5 (2020 ): 262-267
RIS TY - JOUR T1 - The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group AU - Bünyamin Şahin , Abdulgani Şahin Y1 - 2020 PY - 2020 N1 - DO - T2 - Turkish Journal of Science JF - Journal JO - JOR SP - 262 EP - 267 VL - 5 IS - 3 SN - 2587-0971-2587-0971 M3 - UR - Y2 - 2020 ER -
EndNote %0 Turkish Journal of Science The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group %A Bünyamin Şahin , Abdulgani Şahin %T The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group %D 2020 %J Turkish Journal of Science %P 2587-0971-2587-0971 %V 5 %N 3 %R %U
ISNAD Şahin, Bünyamin , Şahin, Abdulgani . "The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group". Turkish Journal of Science 5 / 3 (Aralık 2020): 262-267 .
AMA Şahin B , Şahin A . The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group. TJOS. 2020; 5(3): 262-267.
Vancouver Şahin B , Şahin A . The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group. Turkish Journal of Science. 2020; 5(3): 262-267.
IEEE B. Şahin ve A. Şahin , "The Hosoya Polynomial of the Schreier Graphs of the Grigorchuk Group and the Basilica Group", Turkish Journal of Science, c. 5, sayı. 3, ss. 262-267, Ara. 2021
Makalenin Yazarları
Bünyamin ŞAHİN [1]
Abdulgani ŞAHİN [2]
Makale Gönder
Arşiv
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