Study of Two Types Finite Graphs in KU-Semigroups - Hasan, Elaf R.; Kareem, Fatema F. (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2018)
In this Ë‘work, we present theË‘ notion of the Ë‘graph for a KU-semigroup as theË‘undirected simple graphË‘ with the vertices are the elementsË‘ of and weË‘Ë‘study the Ë‘graph ofË‘ equivalence classesË‘ofË‘ which is determinedË‘ by theË‘ definition equivalenceË‘ relation ofË‘ these verticesË‘, andË‘ then some related Ë‘properties areË‘ given. Several examples are presented and some theorems are proved. ByË‘ usingË‘ the definitionË‘ ofË‘ isomorphicË‘ graph, Ë‘we showË‘ thatË‘ the graphË‘ of equivalence Ë‘classes Ë‘and the Ë‘graphË‘of Ë‘a KU-semigroup Ë‘ areË‘ theË‘ sameË‘, in special cases.