Graph of NG groups not subset of S3 and S4

TL;DR

This paper explores the properties of graphs formed by groups of functions on a set X, specifically those not contained within S3 and S4, and examines their structure and fixed point properties.

Contribution

It introduces a new class of graphs based on groups of mappings outside S3 and S4 and analyzes their structural and fixed point properties.

Findings

Groups of mappings not subset of S3 and S4 form distinct graph structures.

Studied properties of these graphs reveal unique structural characteristics.

Analysis of fixed points provides insights into group actions on sets.

Abstract

In this paper, we introduce and study the graph of the groups of mappings on a set X with respect to function compositions that cannot be subsets of the symmetric groups S3 and S4. Furthermore, we investigate some of the justifications on these groups that have studied in graph theory, and we got good results. Moreover, we consider the graph of these groups by fixed points and study some properties of it.