Research Article

On partial endomorphisms of a star graph

Published in: Quaestiones Mathematicae
Volume 47 , issue 12 , 2024 , pages: 2485–2505

DOI: 10.2989/16073606.2024.2374796

Author(s): Ilinka Dimitrova South-West University “Neofit Rilski”, Bulgaria , Vítor H. Fernandes Universidade Nova de Lisboa, Portugal , Jörg Koppitz Institute of Mathematics and Informatics, Bulgaria

Keywords: 20M20 , 20M10 , 05C12 , 05C25 , Transformations , partial endomorphisms , star graphs , rank

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Abstract

In 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.

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