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22. The core of a vertex-transitive complementary prismMarko Orel, 2023, original scientific article Abstract: The complementary prism ▫$\Gamma \overline{\Gamma}$▫ is obtained from the union of a graph ▫$\Gamma$▫ and its complement ▫$\overline{\Gamma}$▫ where each pair of identical vertices in ▫$\Gamma$▫ and ▫$\overline{\Gamma}$▫ is joined by an edge. It generalizes the Petersen graph, which is the complementary prism of the pentagon. The core of a vertex-transitive complementary prism is studied. In particular, it is shown that a vertex-transitive complementary prism ▫$\Gamma \overline{\Gamma}$▫ is a core, i.e. all its endomorphisms are automorphisms, whenever ▫$\Gamma$▫ is a core or its core is a complete graph.
Keywords: graph homomorphism, complementary prism, self-complementary graph, vertex-transitive graph, core
Published in RUP: 06.11.2023; Views: 888; Downloads: 5
 Full text (305,54 KB) |
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24. The Sierpiński product of graphsJurij 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: 386; Downloads: 3
Full text (526,44 KB) |
25. Vpliv pandemije covida-19 na osnovnošolske otroke : pregled literatureTimea Štravs, Vesna Jug, 2023, review article Abstract: Pregled literature po deskriptivni metodi vključuje 13 raziskav, ki so preučevale posledice pandemije covida-19 na osnovnošolske otroke. Rezultati pregleda so bili v skladu s cilji razvrščeni v štiri pomenske kategorije: Vpliv pandemije na duševno zdravje otrok; Vpliv pandemije na šolski uspeh osnovnošolcev; Povezanost pandemije in fizične aktivnosti otrok ter Drugi vplivi pandemije covida-19, povezani z učenjem na daljavo ter osnovnošolci. Na podlagi pregleda menimo, da je v prihodnje potrebnih še več raziskav na celotnem področju vpliva pandemije na osnovnošolce, še posebej na mlajšo skupino otrok (do 9 let). Zaradi trenutnega prepada v znanju in razumevanju vseh posledic pandemije so nujne longitudinalne raziskave, ki bodo omogočile podrobnejši vpogled v spremembe v izobraževanju, ki so se zgodile pred, med in po pandemiji covida-19.
Keywords: pandemija covida-19, osnovnošolski otroci, duševno zdravje, šolski uspeh, fizična aktivnost
Published in RUP: 06.11.2023; Views: 434; Downloads: 10
Full text (194,41 KB) |
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