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1.
The Sierpiński product of graphs
Jurij Kovič, Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik, 2023, original scientific article

Abstract: 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.
Keywords: Sierpiński graphs, graph products, connectivity, planarity, symmetry
Published in RUP: 06.11.2023; Views: 253; Downloads: 3
.pdf Full text (526,44 KB)

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Agro-food exports variety from the Central and Eastern European countries
Štefan Bojnec, Imre Fertő, 2012, original scientific article

Abstract: This paper analyses the agro-food exports variety from twelve Central and Eastern European countries (CEECs) to the European Union (EU) during the years 1995-2007. The panel regression models explain the agro-food exports by its previous year, income in the importing EU countries, and measure of agro-food export product variety, while the real exŽchange rate appreciation of the CEECcurrencies has negatively influenced agro-food exports. The EU enlargement with the reduction in agricultural protection and the borderless single market has induced agro-food export increases in primary agŽricultural produce and intermediate food-processed products, but less in higher value-added food-processed differentiated products. The impact of increased number of CEECs agro-food product varieties on agro-food export to the EU is positive.
Keywords: export variety, agro-food products, Central and Eastern European countries, European Union
Published in RUP: 15.10.2013; Views: 4968; Downloads: 107
URL Link to full text

10.
On Cayley digraphs on nonisomorphic 2-groups
István Kovács, Mary Agnes Milanič, 2012, original scientific article

Keywords: Cayley digraphs, isomorphisms, abelian groups, wreath products
Published in RUP: 15.10.2013; Views: 2867; Downloads: 209
URL Link to full text

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