The non-commuting graph of a non-central hypergroup

Abstract

The aim of this paper is to construct and study the properties of a certain graph associated with a non-central hypergroup, i.e. a hypergroup having non-commutative the associated fundamental group. The method of the construction of the graph is similar to that one proposed by Paul Erdős, when he defined a graph associated with a non-commutative group. We establish necessary and /or sufficient conditions for the associated graph to be Hamiltonian or planar.

Keywords

• (semi)hypergroup
• hamiltonian graph
• planar graph
• 05c25
• 05c10
• 20n20