Study of Cayley Digraphs over Polygroups

Ali Sanjabi, Morteza Jafarpour, Sarka Hoskova-Mayerova (), Hossien Aghabozorgi and Alena Vagaska ()
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Ali Sanjabi: Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran
Morteza Jafarpour: Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran
Sarka Hoskova-Mayerova: Department of Mathematics and Physics, University of Defence in Brno, Kounicova 65, 662 10 Brno, Czech Republic
Hossien Aghabozorgi: Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran
Alena Vagaska: Faculty of Manufacturing Technologies, Technical University of Košice with a Seat in Prešov, 080 01 Prešov, Slovakia

Mathematics, 2024, vol. 12, issue 17, 1-14

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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