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SPECTRAL INSIGHTS ON ISOLATED DOMINATION AND BINDING NUMBERS IN GRAPHS.

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Title: SPECTRAL INSIGHTS ON ISOLATED DOMINATION AND BINDING NUMBERS IN GRAPHS.
Authors: Manohar, S. H.1,2 manoharsh146@gmail.com, Vijendra, N.1 vijendran397@gmail.com, Boregowda, H. S.1 bgsamarasa@gmail.com
Source: Advances & Applications in Discrete Mathematics. Jul2026, Vol. 43 Issue 5, p661-673. 13p.
Subjects: Graph theory, Dominating set
Abstract: The binding number of a graph quantifies how strongly its vertices are tied together by their neighborhoods. In this paper, we prove that if the binding number, b >1, then every isolated realizing set is an isolated dominating set. We further establish several inequalities relating the binding number and the isolated domination number, and derive bounds involving structural parameters and spectral quantities. Our results highlight a close interplay between domination-type parameters and the binding 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.)
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  Data: SPECTRAL INSIGHTS ON ISOLATED DOMINATION AND BINDING NUMBERS IN GRAPHS.
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  Data: <searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Dominating+set%22">Dominating set</searchLink>
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  Data: The binding number of a graph quantifies how strongly its vertices are tied together by their neighborhoods. In this paper, we prove that if the binding number, b >1, then every isolated realizing set is an isolated dominating set. We further establish several inequalities relating the binding number and the isolated domination number, and derive bounds involving structural parameters and spectral quantities. Our results highlight a close interplay between domination-type parameters and the binding number. [ABSTRACT FROM AUTHOR]
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  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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      – TitleFull: SPECTRAL INSIGHTS ON ISOLATED DOMINATION AND BINDING NUMBERS IN GRAPHS.
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              Text: Jul2026
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