| Naslov: | The Sierpiński domination number |
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| Avtorji: | ID Henning, Michael A. (Avtor)
ID Klavžar, Sandi (Avtor)
ID Kleszcz, Elżbieta (Avtor)
ID Pilśniak, Monika (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (379,57 KB)
MD5: 54929780D0AEF0BB0051A93F1FF77163
 URL - Izvorni URL, za dostop obiščite https://amc-journal.eu/index.php/amc/article/view/2892
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | 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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| Ključne besede: | Sierpiński graph, Sierpiński product, domination number, Sierpiński domination number |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.01.2024 |
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| Leto izida: | 2024 |
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| Št. strani: | 16 str. |
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| Številčenje: | Vol. 24, no. 3, article no. P3.06 |
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| PID: | 20.500.12556/DiRROS-21308  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 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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| Opomba: |
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| Datum objave v DiRROS: | 24.01.2025 |
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| Število ogledov: | 568 |
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| Število prenosov: | 384 |
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| Metapodatki: |    |
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