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An extension of locating-total domination problem and its complexity.

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Title: An extension of locating-total domination problem and its complexity.
Authors: Eswar, N.1 (AUTHOR) jgopal89@gmail.com, Jayagopal, R.1 (AUTHOR) jgopal89@gmail.com
Source: RAIRO: Operations Research (2804-7303). 2024, Vol. 58 Issue 6, p4889-4904. 16p.
Subjects: NP-complete problems, Necklaces, Silicates, Dominating set
Abstract: An r-dominating set (r-total dominating set) of G is a subset S of V (G) for which Nr(u)∩S is non-empty for all u not in S (for all u in V (G)). An r-locating-dominating set (r-locating-total dominating set) of G is an r-dominating set (r-total dominating set) S of G for which Nr(u) ∩S is different from Nr(v) ∩S for all u and v not in S. This paper presents an extension of the locating-total dominating set of G. Further, we establish a lower bound on r-locating-dominating set and r-locating-total dominating set for k-regular graphs, as well as demonstrate that r-locating-total dominating set is an NP-complete problem. Furthermore, the r-locating-dominating set and r-locating-total dominating set problems are discussed for some standard graphs. [ABSTRACT FROM AUTHOR]
Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences 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: An extension of locating-total domination problem and its complexity.
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  Data: <searchLink fieldCode="AR" term="%22Eswar%2C+N%2E%22">Eswar, N.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jgopal89@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Jayagopal%2C+R%2E%22">Jayagopal, R.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jgopal89@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22RAIRO%3A+Operations+Research+%282804-7303%29%22">RAIRO: Operations Research (2804-7303)</searchLink>. 2024, Vol. 58 Issue 6, p4889-4904. 16p.
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  Data: <searchLink fieldCode="DE" term="%22NP-complete+problems%22">NP-complete problems</searchLink><br /><searchLink fieldCode="DE" term="%22Necklaces%22">Necklaces</searchLink><br /><searchLink fieldCode="DE" term="%22Silicates%22">Silicates</searchLink><br /><searchLink fieldCode="DE" term="%22Dominating+set%22">Dominating set</searchLink>
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  Data: An r-dominating set (r-total dominating set) of G is a subset S of V (G) for which Nr(u)∩S is non-empty for all u not in S (for all u in V (G)). An r-locating-dominating set (r-locating-total dominating set) of G is an r-dominating set (r-total dominating set) S of G for which Nr(u) ∩S is different from Nr(v) ∩S for all u and v not in S. This paper presents an extension of the locating-total dominating set of G. Further, we establish a lower bound on r-locating-dominating set and r-locating-total dominating set for k-regular graphs, as well as demonstrate that r-locating-total dominating set is an NP-complete problem. Furthermore, the r-locating-dominating set and r-locating-total dominating set problems are discussed for some standard graphs. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences 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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        Value: 10.1051/ro/2024123
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        Text: English
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        PageCount: 16
        StartPage: 4889
    Subjects:
      – SubjectFull: NP-complete problems
        Type: general
      – SubjectFull: Necklaces
        Type: general
      – SubjectFull: Silicates
        Type: general
      – SubjectFull: Dominating set
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      – TitleFull: An extension of locating-total domination problem and its complexity.
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              Text: 2024
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