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Volume 12
Issue 17
10.3390/math12172711
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Study of Cayley Digraphs over Polygroups

by
Ali Sanjabi
1,
Morteza Jafarpour
1,
Sarka Hoskova-Mayerova
2,*,
Hossien Aghabozorgi
1 and
Alena Vagaska
3,*
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran
2
Department of Mathematics and Physics, University of Defence in Brno, Kounicova 65, 662 10 Brno, Czech Republic
3
Faculty of Manufacturing Technologies, Technical University of Košice with a seat in Prešov, 080 01 Prešov, Slovakia
*
Authors to whom correspondence should be addressed.
Mathematics 2024, 12(17), 2711; https://doi.org/10.3390/math12172711
Submission received: 17 May 2024 / Revised: 8 August 2024 / Accepted: 28 August 2024 / Published: 30 August 2024
Versions Notes

Abstract

In this paper we introduce Cayley digraphs associated to finitely generated polygroups, where the vertices correspond to finite products of the generators of polygroups and the edges to multiplication by vertices and generators. We investigate some properties of the Cayley digraphs, emphasizing connectivity and existence of cycles for each vertex of the Cayley digraphs. Particularly, we identify Cayley digraphs on polygroups derived from conjugate classes of dihedral groups. Moreover, we examine some fundamental illustrative examples of Cayley digraphs through the class of gmg-polygroups.
Keywords: Cayley digraph; gmg-polygroup; dihedral group; connected graph Cayley digraph; gmg-polygroup; dihedral group; connected graph

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MDPI and ACS Style

Sanjabi, A.; Jafarpour, M.; Hoskova-Mayerova, S.; Aghabozorgi, H.; Vagaska, A. Study of Cayley Digraphs over Polygroups. Mathematics 2024, 12, 2711. https://doi.org/10.3390/math12172711

AMA Style

Sanjabi A, Jafarpour M, Hoskova-Mayerova S, Aghabozorgi H, Vagaska A. Study of Cayley Digraphs over Polygroups. Mathematics. 2024; 12(17):2711. https://doi.org/10.3390/math12172711

Chicago/Turabian Style

Sanjabi, Ali, Morteza Jafarpour, Sarka Hoskova-Mayerova, Hossien Aghabozorgi, and Alena Vagaska. 2024. "Study of Cayley Digraphs over Polygroups" Mathematics 12, no. 17: 2711. https://doi.org/10.3390/math12172711

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