| Title: | The Sierpiński domination number |
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| Authors: | ID Henning, Michael A. (Author)
ID Klavžar, Sandi (Author)
ID Kleszcz, Elżbieta (Author)
ID Pilśniak, Monika (Author) |
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| Files: |  PDF - Presentation file, download (379,57 KB)
MD5: 54929780D0AEF0BB0051A93F1FF77163
 URL - Source URL, visit https://amc-journal.eu/index.php/amc/article/view/2892
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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: | Let $G$ and $H$ be graphs and let $f \colon V(G)\rightarrow V(H)$ be a function. The Sierpiński product of $G$ and $H$ with respect to $f$, denoted by $G \otimes _f H$, is defined as the graph on the vertex set $V(G)\times V(H)$, consisting of $|V(G)|$ copies of $H$; for every edge $gg'$ of $G$ there is an edge between copies $gH$ and $g'H$ of $H$ associated with the vertices $g$ and $g'$ of $G$, respectively, of the form $(g,f(g'))(g',f(g))$. In this paper, we define the Sierpiński domination number as the minimum of $\gamma(G\otimes _f H)$ over all functions $f \colon V(G)\rightarrow V(H)$. The upper Sierpiński domination number is defined analogously as the corresponding maximum. After establishing general upper and lower bounds, we determine the upper Sierpiński domination number of the Sierpiński product of two cycles, and determine the lower Sierpiński domination number of the Sierpiński product of two cycles in half of the cases and in the other half cases restrict it to two values. |
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| Keywords: | Sierpiński graph, Sierpiński product, domination number, Sierpiński domination number |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 16 str. |
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| Numbering: | Vol. 24, no. 3, article no. P3.06 |
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| PID: | 20.500.12556/DiRROS-21308  |
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| UDC: | 519.17 |
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| ISSN on article: | 1855-3966 |
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| DOI: | 10.26493/1855-3974.2892.f07 |
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| COBISS.SI-ID: | 202296323 |
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| Note: |
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| Publication date in DiRROS: | 24.01.2025 |
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| Views: | 576 |
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| Downloads: | 386 |
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| Metadata: |    |
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