CHARACTERIZATION OF GRAPHS WITH EQUAL DOMINATION AND INDEPENDENT DOMINATION NUMBERS.
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| Title: | CHARACTERIZATION OF GRAPHS WITH EQUAL DOMINATION AND INDEPENDENT DOMINATION NUMBERS. |
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| Authors: | Bara, Zuraida J.1 zuraidabara0268@gmail.com |
| Source: | Advances & Applications in Discrete Mathematics. Jul2026, Vol. 43 Issue 5, p675-686. 12p. |
| Subjects: | Dominating set, Independent sets, Graph theory, Paths & cycles in graph theory |
| Abstract: | Let G be a finite simple graph. The domination number γ(G) is the minimum cardinality of a dominating set, whereas the independent domination number i(G) is the minimum cardinality of a dominating set that is also independent. Since every independent dominating set is a dominating set, γ (G) ≤ l(G) for every graph G. This paper studies the extremal equality case γ (G) = l(G). We give equivalent characterizations in terms of minimum dominating sets, maximal independent sets, and edge-minimal induced subgraphs on γ-sets. We also prove preservation under disjoint union, determine the equality condition for complete multipartite graphs and joins, and give a separate treatment of paths and cycles, for which the two parameters are equal. The results isolate the structural obstruction to equality: every minimum dominating set must contain adjacent vertices precisely when the independent domination number strictly exceeds the domination number. [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: CHARACTERIZATION OF GRAPHS WITH EQUAL DOMINATION AND INDEPENDENT DOMINATION NUMBERS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bara%2C+Zuraida+J%2E%22">Bara, Zuraida J.</searchLink><relatesTo>1</relatesTo><i> zuraidabara0268@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Advances+%26+Applications+in+Discrete+Mathematics%22">Advances & Applications in Discrete Mathematics</searchLink>. Jul2026, Vol. 43 Issue 5, p675-686. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Dominating+set%22">Dominating set</searchLink><br /><searchLink fieldCode="DE" term="%22Independent+sets%22">Independent sets</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Paths+%26+cycles+in+graph+theory%22">Paths & cycles in graph theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Let G be a finite simple graph. The domination number γ(G) is the minimum cardinality of a dominating set, whereas the independent domination number i(G) is the minimum cardinality of a dominating set that is also independent. Since every independent dominating set is a dominating set, γ (G) ≤ l(G) for every graph G. This paper studies the extremal equality case γ (G) = l(G). We give equivalent characterizations in terms of minimum dominating sets, maximal independent sets, and edge-minimal induced subgraphs on γ-sets. We also prove preservation under disjoint union, determine the equality condition for complete multipartite graphs and joins, and give a separate treatment of paths and cycles, for which the two parameters are equal. The results isolate the structural obstruction to equality: every minimum dominating set must contain adjacent vertices precisely when the independent domination number strictly exceeds the domination number. [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: 10.17654/0974165826043 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 675 Subjects: – SubjectFull: Dominating set Type: general – SubjectFull: Independent sets Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Paths & cycles in graph theory Type: general Titles: – TitleFull: CHARACTERIZATION OF GRAPHS WITH EQUAL DOMINATION AND INDEPENDENT DOMINATION NUMBERS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bara, Zuraida J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 09741658 Numbering: – Type: volume Value: 43 – Type: issue Value: 5 Titles: – TitleFull: Advances & Applications in Discrete Mathematics Type: main |
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