ON THE SZEGED INDEX AND ITS NON-COMMUTING GRAPH

• Published in: Jurnal Teknologi
• Main Author: Alimon N.I.; Sarmin N.H.; Erfanian A.
• Format: Article
• Language: English
• Published: Penerbit UTM Press 2023
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85159059661&doi=10.11113%2fjurnalteknologi.v85.19221&partnerID=40&md5=c666d2f8244df9b7df77fbd45064e8fa

In chemistry, the molecular structure can be represented as a graph. Based on the information from the graph, its characterization can be determined by computing the topological index. Topological index is a numerical value that can be computed by using some algorithms and properties of the graph. Meanwhile, the non-commuting graph is a graph, in which two distinct vertices are adjacent if and only if they do not commute, where it is made up of the non-central elements in a group as a vertex set. In this paper, the Szeged index of the non-commuting graph of some finite groups are computed. This paper focuses on three finite groups which are the quasidihedral groups, the dihedral groups, and the generalized quaternion groups. The construction of the graph is done by using Maple software. In finding the Szeged index, some of the previous results and properties of the graph for the quasidihedral groups, the dihedral groups, and the generalized quaternion groups are used. The generalisation of the Szeged index of the non-commuting graph is then established for the aforementioned groups. The results are then applied to find the Szeged index of the non-commuting graph of ammonia molecule. © 2023 Penerbit UTM Press. All rights reserved.