THE g-NON-COMMUTING GRAPH FOR SOME FINITE GROUPS AND THEIR RANDIC INDEX.
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| Title: | THE g-NON-COMMUTING GRAPH FOR SOME FINITE GROUPS AND THEIR RANDIC INDEX. |
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| Authors: | Roslly, Siti Rosllydia Dania1, Alimon, Nur Idayu2, Mohammad, Siti Afiqah3, Sarmin, Nor Haniza4 |
| Source: | Advances & Applications in Discrete Mathematics. Apr2026, Vol. 43 Issue 3, p299-320. 22p. |
| Subjects: | Finite groups, Molecular graphs |
| Abstract: | A molecular graph is an essentially non-numerical mathematical object, and to link molecular topology with molecular properties, its information is converted into a numerical characteristic called a topological index (TOI). The study on TOIs has grown significantly since 1947 and many types of topological indices have been developed until recently. The g-non-commuting graph is an extension of the noncommuting graph. For a finite group G and a fixed element, G ∈ g the g-non-commuting graph is defined with the vertex set G, where two distinct vertices x and y are adjacent if [x,y] ≠ g, and [x,y] ≠ g-1. Meanwhile, the Randić index, a degree-based TOI, is defined as the sum of the reciprocal square roots of the product of the degrees of two adjacent vertices in a graph. In this study, the general form of the g-non-commuting graph associated to the dihedral, the generalized quaternion, and the quasidihedral groups, are introduced. Then, based on these graphs, their Randić indices are determined and some examples are also presented to illustrate the main theorems. These results can be beneficial to predict the physicochemical properties of the molecules. [ABSTRACT FROM AUTHOR] |
| Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: THE g-NON-COMMUTING GRAPH FOR SOME FINITE GROUPS AND THEIR RANDIC INDEX. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Roslly%2C+Siti+Rosllydia+Dania%22">Roslly, Siti Rosllydia Dania</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Alimon%2C+Nur+Idayu%22">Alimon, Nur Idayu</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Mohammad%2C+Siti+Afiqah%22">Mohammad, Siti Afiqah</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Sarmin%2C+Nor+Haniza%22">Sarmin, Nor Haniza</searchLink><relatesTo>4</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Advances+%26+Applications+in+Discrete+Mathematics%22">Advances & Applications in Discrete Mathematics</searchLink>. Apr2026, Vol. 43 Issue 3, p299-320. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+groups%22">Finite groups</searchLink><br /><searchLink fieldCode="DE" term="%22Molecular+graphs%22">Molecular graphs</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A molecular graph is an essentially non-numerical mathematical object, and to link molecular topology with molecular properties, its information is converted into a numerical characteristic called a topological index (TOI). The study on TOIs has grown significantly since 1947 and many types of topological indices have been developed until recently. The g-non-commuting graph is an extension of the noncommuting graph. For a finite group G and a fixed element, G ∈ g the g-non-commuting graph is defined with the vertex set G, where two distinct vertices x and y are adjacent if [x,y] ≠ g, and [x,y] ≠ g-1. Meanwhile, the Randić index, a degree-based TOI, is defined as the sum of the reciprocal square roots of the product of the degrees of two adjacent vertices in a graph. In this study, the general form of the g-non-commuting graph associated to the dihedral, the generalized quaternion, and the quasidihedral groups, are introduced. Then, based on these graphs, their Randić indices are determined and some examples are also presented to illustrate the main theorems. These results can be beneficial to predict the physicochemical properties of the molecules. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Advances & Applications in Discrete Mathematics is the property of Pushpa Publishing House and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.17654/0974165826020 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 299 Subjects: – SubjectFull: Finite groups Type: general – SubjectFull: Molecular graphs Type: general Titles: – TitleFull: THE g-NON-COMMUTING GRAPH FOR SOME FINITE GROUPS AND THEIR RANDIC INDEX. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Roslly, Siti Rosllydia Dania – PersonEntity: Name: NameFull: Alimon, Nur Idayu – PersonEntity: Name: NameFull: Mohammad, Siti Afiqah – PersonEntity: Name: NameFull: Sarmin, Nor Haniza IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 09741658 Numbering: – Type: volume Value: 43 – Type: issue Value: 3 Titles: – TitleFull: Advances & Applications in Discrete Mathematics Type: main |
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