20.500.12556/DiRROS-18479 The Sierpiński product of graphs In this paper we introduce a product-like operation that generalizes the construction of the generalized Sierpiński graphs. Let $G$, $H$ be graphs and let $f: V(G) \to V(H)$ be a function. Then the Sierpiński product of graphs $G$ 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 $\{g, g'\}$ of $G$ there is an edge between copies $gH$ and $g'H$ of form $\{(g, f(g'), (g', f(g))\}$. Some basic properties of the Sierpiński product are presented. In particular, we show that the graph $G\otimes_f H$ is connected if and only if both graphs $G$ and $H$ are connected and we present some conditions that $G, \, H$ must fulfill for $G\otimes_f H$ to be planar. As for symmetry properties, we show which automorphisms of $G$ and $H$ extend to automorphisms of $G\otimes_f H$. In several cases we can also describe the whole automorphism group of the graph $G\otimes_f H$. Finally, we show how to extend the Sierpiński product to multiple factors in a natural way. By applying this operation $n$ times to the same graph we obtain an alternative approach to the well-known $n$-th generalized Sierpiński graph. Sierpiński graphs graph products connectivity planarity symmetry grafi Sierpińskega produkti grafov povezanost ravninskost simetrija true false true Angleški jezik Slovenski jezik Neznano 2024-03-19 14:06:23 2024-03-19 14:06:23 2024-03-20 03:39:24 0000-00-00 00:00:00 2023 0 0 Soavtorji: Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik; art. P1.01 (25 str.) no. 1 Vol. 23 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-01-01 519.17 1855-3966 10.26493/1855-3974.1970.29e 143319043 amc_1970-1.pdf amc_1970-1.pdf 1 5B2EE11E73604A9130960C81137B6CF1 1aef369af40b2b87643292ca8cf32b3785c1f107d0d7b9a330002d71cf041697 ee5e99be-e5f1-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25177 https://amc-journal.eu/index.php/amc/article/view/1970/1763 0 e8233952-e5f1-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25176 Inštitut za matematiko, fiziko in mehaniko 0 0 0