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On the Szeged index and its non-commuting graph

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. M...

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Main Authors: Alimon, Nur Idayu, Sarmin, Nor Haniza, Erfanian, Ahmad
Format: Article
Language:English
Published: Penerbit UTM Press 2023
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/105182/1/NorHanizaSarmin2023_OntheSzegedIndexanditsNonCommuting.pdf
http://eprints.utm.my/105182/
http://dx.doi.org/10.11113/jurnalteknologi.v85.19221
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spelling my.utm.1051822024-04-07T04:14:14Z http://eprints.utm.my/105182/ On the Szeged index and its non-commuting graph Alimon, Nur Idayu Sarmin, Nor Haniza Erfanian, Ahmad QA Mathematics 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. Penerbit UTM Press 2023-05 Article PeerReviewed application/pdf en http://eprints.utm.my/105182/1/NorHanizaSarmin2023_OntheSzegedIndexanditsNonCommuting.pdf Alimon, Nur Idayu and Sarmin, Nor Haniza and Erfanian, Ahmad (2023) On the Szeged index and its non-commuting graph. Jurnal Teknologi, 85 (3). pp. 105-110. ISSN 0127-9696 http://dx.doi.org/10.11113/jurnalteknologi.v85.19221 DOI:10.11113/jurnalteknologi.v85.19221
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Alimon, Nur Idayu
Sarmin, Nor Haniza
Erfanian, Ahmad
On the Szeged index and its non-commuting graph
description 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.
format Article
author Alimon, Nur Idayu
Sarmin, Nor Haniza
Erfanian, Ahmad
author_facet Alimon, Nur Idayu
Sarmin, Nor Haniza
Erfanian, Ahmad
author_sort Alimon, Nur Idayu
title On the Szeged index and its non-commuting graph
title_short On the Szeged index and its non-commuting graph
title_full On the Szeged index and its non-commuting graph
title_fullStr On the Szeged index and its non-commuting graph
title_full_unstemmed On the Szeged index and its non-commuting graph
title_sort on the szeged index and its non-commuting graph
publisher Penerbit UTM Press
publishDate 2023
url http://eprints.utm.my/105182/1/NorHanizaSarmin2023_OntheSzegedIndexanditsNonCommuting.pdf
http://eprints.utm.my/105182/
http://dx.doi.org/10.11113/jurnalteknologi.v85.19221
_version_ 1797905956342857728
score 13.211869

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