20.500.12556/RUP-19869-db236bc0-7b5f-0e1b-342e-58c3685a1410 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 true true false Angleški jezik Angleški jezik Neznano 2023-11-06 09:31:13 2023-11-06 09:31:16 2024-03-01 14:43:21 0000-00-00 00:00:00 2023 0 0 art. P1.01 (25 str.) no. 1 Vol. 23 2023 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2023-01-01 519.17 1855-3966 10.26493/1855-3974.1970.29e 143319043 AMC_Kovic_Pisanski_Zemljic_Zitnik_i2022.pdf AMC_Kovic_Pisanski_Zemljic_Zitnik_i2022.pdf 1 4877F5DF98ECDA9B5FD0C4CCEE915376 a8b2ea565366055d51f1b558152ff25d4901ac0d35232e1d3710a3f378f1d4c3 423c6862-7c7f-11ee-b5df-005056bf369b https://repozitorij.upr.si/Dokument.php?lang=slv&id=28710 Založba Univerze na Primorskem 0 0 0