525 KB66 KB180 KB6 KB200820252023Kovič, JurijPisanski, TomažZemljič, Sara SabrinaŽitnik, Arjanaštevilka:1letnik:23art. P1.01 (25 str.)DOI:10.26493/1855-3974.1970.29eCOBISSID_HOST:143319043ISSN:1855-3966URN:URN:NBN:SI:doc-C1KEUNTZenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaconnectivitygraph productsplanaritySierpiński graphssymmetryThe 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 graphTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije