The topological indices of the non-commuting graph for symmetric groups

• Main Authors: Alimon, N. I., Sarmin, N. H., Erfanian, A.
• Format: Article
• Language: English
• Published: Akademi Sains Malaysia 2020
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/86579/1/NurIdayuAlimon2020_TheTopologicalIndicesoftheNonCommuting.pdf; http://eprints.utm.my/id/eprint/86579/; https://dx.doi.org/10.32802/asmscj.2020.sm26(1.28)

Topological indices are the numerical values that can be calculated from a graph and it is calculated based on the molecular graph of a chemical compound. It is often used in chemistry to analyse the physical properties of the molecule which can be represented as a graph with a set of vertices and edges. 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 they do not commute. The symmetric group, denoted as, is a set of all permutation under composition. In this paper, two of the topological indices, namely the Wiener index and the Zagreb index of the non-commuting graph for symmetric groups of order 6 and 24 are determined.