Presentations for monoids of partial endomorphisms of a star graph

TL;DR

This paper provides algebraic presentations for various monoids of partial endomorphisms of a finite star graph, expanding understanding of their structure and relationships.

Contribution

It introduces explicit presentations for monoids of all partial endomorphisms, weak endomorphisms, and their injective and strong variants of a star graph.

Findings

Presented algebraic structures for each monoid type

Derived generators and relations for the monoids

Enhanced understanding of endomorphism monoids in graph theory

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 exhibit a presentation for each of them.