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- Title
On Two-Sided Cayley Graphs of Semigroups and Groups.
- Authors
Hassani Hajivand, Farshad; Khosravi, Behnam
- Abstract
In this paper, first we introduce the notion of two-sided Cayley graph of a semigroup. Then, we investigate some fundamental properties of these graphs and we use our results to give partial answers to some problems raised by Iradmusa and Praeger about two-sided group graphs (two-sided Cayley graphs of groups). Specially, as a consequence of our results, we determine all undirected two-sided Cayley graphs of groups which are connected. Furthermore, by introducing the notion of color-preserving automorphisms of a two-sided Cayley graph of a semigroup (group) and calculating them under some assumptions, we determine the family of color-vertex transitive two-sided Cayley graphs of semigroups (groups).
- Subjects
CAYLEY graphs; AUTOMORPHISMS
- Publication
Annals of Combinatorics, 2023, Vol 27, Issue 2, p413
- ISSN
0218-0006
- Publication type
Article
- DOI
10.1007/s00026-022-00618-y