Constructing non-commuting graph of symmetric groups by using maples software

Abstract

Maple is a symbolic and numeric computing environment and also a multi-paradigm programming language. It is also covers other aspects of technical computing such as visualisation and matrix computation. Maple can be used to construct the graph related to groups which involves the package of group theory and graph theory. The aim of this paper is to present the Maple’s coding in constructing the non- commuting graph of the symmetric groups. Meanwhile, the non- commuting graph is the graph of vertex set whose vertices are non-central elements and two distinct vertices are joined by an edge if and only they do not commute. The symmetric group, denoted by is a group of permutations on a set with elements. This paper only focuses on finding the non-commuting graph of symmetric groups of order six and 24.