Super graphs on groups, II.
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| Title: | Super graphs on groups, II. |
|---|---|
| Authors: | Arunkumar, G.1 (AUTHOR) arun.maths123@gmail.com, Cameron, Peter J.2 (AUTHOR) pjc20@st-andrews.ac.uk, Nath, Rajat Kanti1,3 (AUTHOR) rajatkantinath@yahoo.com |
| Source: | Discrete Applied Mathematics. Dec2024, Vol. 359, p371-382. 12p. |
| Subjects: | Authors |
| Abstract: | In an earlier paper, the authors considered three types of graphs, and three equivalence relations, defined on a group, viz. the power graph, enhanced power graph, and commuting graph, and the relations of equality, conjugacy, and same order; for each choice of a graph type A and an equivalence relation B , there is a graph, the B super A graph defined on G. The resulting nine graphs (of which eight were shown to be in general distinct) form a two-dimensional hierarchy. In the present paper, we consider these graphs further. We prove universality properties for the conjugacy supergraphs of various types, adding the nilpotent, solvable and enhanced power graphs to the commuting graphs considered in the rest of the paper, and also examine their relation to the invariably generating graph of the group. We also show that supergraphs can be expressed as graph compositions, in the sense of Schwenk, and use this representation to calculate their Wiener index. We illustrate these by computing Wiener index of equality supercommuting and conjugacy supercommuting graphs for dihedral and dicyclic groups. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 180492633 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Super graphs on groups, II. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Arunkumar%2C+G%2E%22">Arunkumar, G.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> arun.maths123@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Cameron%2C+Peter+J%2E%22">Cameron, Peter J.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> pjc20@st-andrews.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Nath%2C+Rajat+Kanti%22">Nath, Rajat Kanti</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> rajatkantinath@yahoo.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Dec2024, Vol. 359, p371-382. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Authors%22">Authors</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In an earlier paper, the authors considered three types of graphs, and three equivalence relations, defined on a group, viz. the power graph, enhanced power graph, and commuting graph, and the relations of equality, conjugacy, and same order; for each choice of a graph type A and an equivalence relation B , there is a graph, the B super A graph defined on G. The resulting nine graphs (of which eight were shown to be in general distinct) form a two-dimensional hierarchy. In the present paper, we consider these graphs further. We prove universality properties for the conjugacy supergraphs of various types, adding the nilpotent, solvable and enhanced power graphs to the commuting graphs considered in the rest of the paper, and also examine their relation to the invariably generating graph of the group. We also show that supergraphs can be expressed as graph compositions, in the sense of Schwenk, and use this representation to calculate their Wiener index. We illustrate these by computing Wiener index of equality supercommuting and conjugacy supercommuting graphs for dihedral and dicyclic groups. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. 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: 10.1016/j.dam.2024.09.012 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 371 Subjects: – SubjectFull: Authors Type: general Titles: – TitleFull: Super graphs on groups, II. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Arunkumar, G. – PersonEntity: Name: NameFull: Cameron, Peter J. – PersonEntity: Name: NameFull: Nath, Rajat Kanti IsPartOfRelationships: – BibEntity: Dates: – D: 31 M: 12 Text: Dec2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 0166218X Numbering: – Type: volume Value: 359 Titles: – TitleFull: Discrete Applied Mathematics Type: main |
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