20.500.12556/RUL-166777 The Sierpiński domination number 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. Sierpiński graph Sierpiński product domination number Sierpiński domination number graf Sierpińskega Sierpińskijev produkt dominacijsko število Sierpińskijevo dominacijsko število true false true Angleški jezik Slovenski jezik Članek v reviji 2025-01-24 11:04:19 2025-01-24 11:04:21 2025-01-25 04:13:10 0000-00-00 00:00:00 2024 0 0 16 str. no. 3, article no. P3.06 Vol. 24 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-01-01 519.17 1855-3966 10.26493/1855-3974.2892.f07 202296323 amc_2892-1.pdf amc_2892-1.pdf 1 1F65700F8478AF0754E4AF81EF6B7AD3 c13100b161c1d1a7b4320118849e5d288e2b62e68cca2e6bb902124c514e0441 2911f1eb-da43-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=198675 https://amc-journal.eu/index.php/amc/article/view/2892 1 c9b85268-da39-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=198665 Fakulteta za matematiko in fiziko 0 0 0