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

#### Bünyamin ŞAHİN [1] , Abdulgani ŞAHİN [2]

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.
Basilica group, Grigorchuk group, Hosoya polynomial, Schreier graph
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Birincil Dil en Fen Volume V Issue III 2020 Orcid: 0000-0003-1094-5481Yazar: Bünyamin ŞAHİNKurum: SELÇUK ÜNİVERSİTESİÜlke: Turkey Orcid: 0000-0002-9446-7431Yazar: Abdulgani ŞAHİN (Sorumlu Yazar)Kurum: Ağrı İbrahim Çeçen ÜniversitesiÜlke: Turkey Yayımlanma Tarihi : 30 Aralık 2020
 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 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

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