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1.
The core of a vertex-transitive complementary prism
Marko 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: 685; Downloads: 3
.pdf Full text (305,54 KB)

2.
On girth-biregular graphs
György Kiss, Štefko Miklavič, Tamás Szőnyi, 2023, original scientific article

Keywords: girth cycle, girth-biregular graph, steiner system, generalized polygons
Published in RUP: 06.11.2023; Views: 229; Downloads: 3
.pdf Full text (429,83 KB)

3.
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: 232; Downloads: 3
.pdf Full text (526,44 KB)

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Analiza blagovnih trgov : pristop teorije grafov
Luka Pavlović, 2023, master's thesis

Keywords: graph, minimum spanning tree, strenght, betwenness, distance, commodites
Published in RUP: 25.08.2023; Views: 451; Downloads: 4
.pdf Full text (1,20 MB)

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On a conjecture about the ratio of Wiener index in iterated line graphs
Katarína Hriňáková, Martin Knor, Riste Škrekovski, 2018, original scientific article

Keywords: Wiener index, line graph, tree, iterated line graph
Published in RUP: 03.01.2022; Views: 1001; Downloads: 24
.pdf Full text (391,35 KB)

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