20.500.12556/DiRROS-18195 Resolvability and convexity properties in the Sierpiński product of graphs 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 $(g,f(g'))(g',f(g))$. The Sierpiński metric dimension and the upper Sierpiński metric dimension of two graphs are determined. Closed formulas are determined for Sierpiński products of trees, and for Sierpiński products of two cycles where the second factor is a triangle. We also prove that the layers with respect to the second factor in a Sierpiński product graph are convex. Sierpiński product of graphs metric dimension trees convex subgraph Sierpinskijev produkt grafov metrična dimenzija drevesa konveksni podgrafi true false true Angleški jezik Slovenski jezik Neznano 2024-02-16 12:32:18 2024-02-16 12:32:19 2024-02-17 03:41:34 0000-00-00 00:00:00 2024 0 0 Spletna objava: 18. 11. 2023; 17 str. iss. 1, article no. 3 Vol. 21 Jan. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-01-01 519.17 1660-5446 10.1007/s00009-023-02544-6 172901379 https://link.springer.com/article/10.1007/s00009-023-02544-6 1 ab1be808-ccb6-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24707 s00009-023-02544-6.pdf s00009-023-02544-6.pdf 1 074DE5ECE31FEB8F337B464DEC07BA72 4e581ed0696db479ed099b655fbfdae16935516e7ffc75ef6f10693bf60d388c 4f4a5eb6-ccb7-11ee-aa6e-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24708 Inštitut za matematiko, fiziko in mehaniko 0 0 0