• Nur Idayu Alimon Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Johor Branch, Pasir Gudang Campus, Bandar Sri Alam 81750 Masai, Johor, Malaysia https://orcid.org/0000-0002-3329-7897
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia (UTM), 81310 Johor Bahru, Johor, Malaysia https://orcid.org/0000-0003-4291-5746
  • Ahmad Erfanian Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran https://orcid.org/0000-0002-9637-1417




Szeged index, non-commuting graph, dihedral groups, generalized quaternion groups, quasidihedral groups


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.


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How to Cite

Alimon, N. I., Sarmin, N. H. ., & Erfanian, A. . (2023). ON THE SZEGED INDEX AND ITS NON-COMMUTING GRAPH. Jurnal Teknologi, 85(3), 105–110. https://doi.org/10.11113/jurnalteknologi.v85.19221



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