| Title: | 2-rainbow independent domination in complementary prisms |
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| Authors: | ID Božović, Dragana (Author)
ID Radić, Gordana (Author)
ID Tepeh, Aleksandra (Author) |
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| Files: |  PDF - Presentation file, download (366,61 KB)
MD5: 2642E69DD7AF494D32790AD0C3C92684
 URL - Source URL, visit https://dk.um.si/IzpisGradiva.php?id=92600
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | A function $f$ that assigns values from the set $\{0, 1, 2\}$ to each vertex of a graph is called a $2$-rainbow independent dominating function, if the vertices assigned the value $1$ form an independent set, the vertices assigned the value $2$ form another independent set, and every vertex to which $0$ is assigned has at least one neighbor in each of the mentioned independent sets. The weight of this function is the total number of vertices assigned nonzero values. The $2$-rainbow independent domination number of $G$, $\gamma_{{\rm ri}2}(G)$, is the minimum weight of such a function. Motivated by a real-life application, we study the $2$-rainbow independent domination number of the complementary prism $G \overline{G}$ of a graph $G$, which is constructed by taking $G$ and its complement $\overline{G}$, and then adding edges between corresponding vertices. We provide tight bounds for $\gamma_{{\rm ri}2}(G \overline{G})$, and characterize graphs for which the lower bound, i.e. $\max \{ \gamma_{{\rm ri}2}(G), \gamma_{{\rm ri}2}(\overline{G})\}+1$, is attained. The obtained results can, in practice, enable the prediction of the cost estimate for a given communication or surveillance network. |
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| Keywords: | graph theory, domination, 2-rainbow independent domination, complementary prism |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.04.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 13 str. |
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| Numbering: | Vol. 44, iss. 5, [article no.] 235 |
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| PID: | 20.500.12556/DiRROS-22123  |
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| UDC: | 519.17 |
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| ISSN on article: | 1807-0302 |
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| DOI: | 10.1007/s40314-025-03189-9 |
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| COBISS.SI-ID: | 233075971 |
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| Note: |
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| Publication date in DiRROS: | 28.04.2025 |
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| Views: | 560 |
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| Downloads: | 277 |
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| Metadata: |    |
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