Presentations for monoids of endomorphisms of a star graph

TL;DR

This paper provides algebraic presentations for various monoids of endomorphisms associated with a finite star graph, including weak and strong variants, enhancing understanding of their algebraic structure.

Contribution

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

Findings

Presented algebraic structures for each monoid type.

Derived generators and relations for the monoids.

Enhanced understanding of endomorphism monoids of star graphs.

Abstract

In this paper, we consider the monoids of all endomorphisms, of all weak endomorphisms, of all strong endomorphisms and of all 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.