Secure Integer Domination in Generalized Petersen Graphs.
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| Title: | Secure Integer Domination in Generalized Petersen Graphs. |
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| Authors: | L., Gowtham Priya1 gowthampriya.28@gmail.com, K. A., Venkatesh2 ka.venkatesh@alliance.edu.in |
| Source: | IAENG International Journal of Applied Mathematics. Jul2026, Vol. 56 Issue 7, p2817-2822. 6p. |
| Subjects: | Petersen graphs, Dominating set, Graph theory, Regular graphs |
| Abstract: | Secure integer domination is a strengthening of classical domination that combines the concepts of integer domination and secure domination. In this paper we investigate the secure integer domination number of regular graphs, with particular focus on generalized Petersen graphs P(n, k). Using a double counting argument on closed neighborhoods, we establish a general lower bound for an r-regular graph G of order n:We also characterize the case of equality in terms of balanced closed neighborhood sums. As an application, the results are specialized to cubic graphs and generalized Petersen graphs, for which explicit values and bounds of the secure integer domination number are obtained. These results extend known relationships between classical domination, secure domination, and integer domination in structured graphs. [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 |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 195026913 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Secure Integer Domination in Generalized Petersen Graphs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22L%2E%2C+Gowtham+Priya%22">L., Gowtham Priya</searchLink><relatesTo>1</relatesTo><i> gowthampriya.28@gmail.com</i><br /><searchLink fieldCode="AR" term="%22K%2E+A%2E%2C+Venkatesh%22">K. A., Venkatesh</searchLink><relatesTo>2</relatesTo><i> ka.venkatesh@alliance.edu.in</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>. Jul2026, Vol. 56 Issue 7, p2817-2822. 6p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Petersen+graphs%22">Petersen graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Dominating+set%22">Dominating set</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Regular+graphs%22">Regular graphs</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Secure integer domination is a strengthening of classical domination that combines the concepts of integer domination and secure domination. In this paper we investigate the secure integer domination number of regular graphs, with particular focus on generalized Petersen graphs P(n, k). Using a double counting argument on closed neighborhoods, we establish a general lower bound for an r-regular graph G of order n:We also characterize the case of equality in terms of balanced closed neighborhood sums. As an application, the results are specialized to cubic graphs and generalized Petersen graphs, for which explicit values and bounds of the secure integer domination number are obtained. These results extend known relationships between classical domination, secure domination, and integer domination in structured graphs. [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: 2817 Subjects: – SubjectFull: Petersen graphs Type: general – SubjectFull: Dominating set Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Regular graphs Type: general Titles: – TitleFull: Secure Integer Domination in Generalized Petersen Graphs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: L., Gowtham Priya – PersonEntity: Name: NameFull: K. A., Venkatesh IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 56 – Type: issue Value: 7 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
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