Mathematics (Aug 2024)

Study of Cayley Digraphs over Polygroups

  • Ali Sanjabi,
  • Morteza Jafarpour,
  • Sarka Hoskova-Mayerova,
  • Hossien Aghabozorgi,
  • Alena Vagaska

DOI
https://doi.org/10.3390/math12172711
Journal volume & issue
Vol. 12, no. 17
p. 2711

Abstract

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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.

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