Notes on the Equitable Graph of Type I of a Group.
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| Title: | Notes on the Equitable Graph of Type I of a Group. |
|---|---|
| Authors: | Ma, Xuanlong1 xuanlma@xsyu.edu.cn, Zhang, Bin2 zhangbata@126.com, Zhai, Liangliang1 zhailiang111@126.com, Pan, Junyao3 junyaopan@126.com |
| Source: | IAENG International Journal of Applied Mathematics. Apr2026, Vol. 56 Issue 4, p1242-1247. 6p. |
| Subjects: | Finite groups, Planar graphs, Graph theory, Group theory, Graph connectivity |
| Abstract: | Given a finite group G, the equitable graph of type I of G is a simple graph whose vertex set is G, in which distinct a, b ∈ G are adjacent whenever |o(a)-o(b)| ≤ min{o(a), o(b)}, where o(a) and o(b) are the orders of a and b, respectively. In this paper, we discuss some properties of the equitable graph of type I of a finite group. More specifically, we first obtain a few necessary and sufficient conditions for an equitable graphs of type I to be connected. Then, we classify all finite groups whose equitable graph of type I is planar. Finally, we give a complete classification for toroidal equitable graphs of type I. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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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| Header | DbId: egs DbLabel: Engineering Source An: 192720712 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Notes on the Equitable Graph of Type I of a Group. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Ma%2C+Xuanlong%22">Ma, Xuanlong</searchLink><relatesTo>1</relatesTo><i> xuanlma@xsyu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Bin%22">Zhang, Bin</searchLink><relatesTo>2</relatesTo><i> zhangbata@126.com</i><br /><searchLink fieldCode="AR" term="%22Zhai%2C+Liangliang%22">Zhai, Liangliang</searchLink><relatesTo>1</relatesTo><i> zhailiang111@126.com</i><br /><searchLink fieldCode="AR" term="%22Pan%2C+Junyao%22">Pan, Junyao</searchLink><relatesTo>3</relatesTo><i> junyaopan@126.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Apr2026, Vol. 56 Issue 4, p1242-1247. 6p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+groups%22">Finite groups</searchLink><br /><searchLink fieldCode="DE" term="%22Planar+graphs%22">Planar graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Group+theory%22">Group theory</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+connectivity%22">Graph connectivity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Given a finite group G, the equitable graph of type I of G is a simple graph whose vertex set is G, in which distinct a, b ∈ G are adjacent whenever |o(a)-o(b)| ≤ min{o(a), o(b)}, where o(a) and o(b) are the orders of a and b, respectively. In this paper, we discuss some properties of the equitable graph of type I of a finite group. More specifically, we first obtain a few necessary and sufficient conditions for an equitable graphs of type I to be connected. Then, we classify all finite groups whose equitable graph of type I is planar. Finally, we give a complete classification for toroidal equitable graphs of type I. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 6 StartPage: 1242 Subjects: – SubjectFull: Finite groups Type: general – SubjectFull: Planar graphs Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Group theory Type: general – SubjectFull: Graph connectivity Type: general Titles: – TitleFull: Notes on the Equitable Graph of Type I of a Group. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ma, Xuanlong – PersonEntity: Name: NameFull: Zhang, Bin – PersonEntity: Name: NameFull: Zhai, Liangliang – PersonEntity: Name: NameFull: Pan, Junyao IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 56 – Type: issue Value: 4 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
| ResultId | 1 |
