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Generalized Cayley graphs over polygroups. (English) Zbl 1476.20064

Summary: Polygroups are a generalization of groups in which the composition of any two elements are a non-empty set. In this paper, first we recall the concept of polygroups and introduce a new construction for building a polygroup from a polygroup and a non-empty set. Then we study the concept of generalized Cayley graphs over polygroups, say GCP-graphs. Then we prove some properties of them in order to answer this question: which simple graphs are GCP-graphs? Finally, we prove that every simple graph of order at most five is a GCP-graph.

MSC:

20N20 Hypergroups
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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