On partial endomorphisms of a star graph

AbstractIn this paper we consider the monoids of all partial endomorphisms, of all partial weak endomorphisms, of all injective partial endomorphisms, of all partial strong endomorphisms and of all partial strong weak endomorphisms of a star graph with a finite number of vertices. Our main objective is to determine their ranks. We also describe their Green's relations, calculate their cardinalities and study their regularity.Mathematics Subject Classification (2020): 20M2020M1005C1205C25Key words: Transformationspartial endomorphismsstar graphsrank