1. Mutual-visibility problems in Kneser and Johnson graphsGülnaz Boruzanlı Ekinci, Csilla Bujtás, 2025, original scientific article Abstract: Let G be a connected graph and X ⊆ V(G). By definition, two vertices u and v are X-visible in G if there exists a shortest u, v-path with all internal vertices being outside of the set X. The largest size of X such that any two vertices of G (resp. any two vertices from X) are X-visible is the total mutual-visibility number (resp. the mutual-visibility number) of G.
In this paper, we determine the total mutual-visibility number of Kneser graphs, bipartite Kneser graphs, and Johnson graphs. The formulas proved for Kneser, and bipartite Kneser graphs are related to the size of transversal-critical uniform hypergraphs, while the total mutual-visibility number of Johnson graphs is equal to a hypergraph Turán number. Exact values or estimations for the mutual-visibility number over these graph classes are also established.
Keywords: mutual-visibility set, total mutual-visibility set, Kneser graph, bipartite Kneser graph, Johnson graph, Turán-type problem, covering design
Published in RUP: 22.10.2025; Views: 1182; Downloads: 14
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3. Splittable and unsplittable graphs and configurationsNino Bašić, Jan Grošelj, Branko Grünbaum, Tomaž Pisanski, 2019, original scientific article Abstract: We prove that there exist infinitely many splittable and also infinitely many unsplittable cyclic ▫$(n_3)$▫ configurations. We also present a complete study of trivalent cyclic Haar graphs on at most 60 vertices with respect to splittability. Finally, we show that all cyclic flag-transitive configurations with the exception of the Fano plane and the Möbius-Kantor configuration are splittable.
Keywords: configuration of points and lines, unsplittable configuration, unsplittable graph, independent set, Levi graph, Grünbaum graph, splitting type, cyclic Haar graph
Published in RUP: 03.01.2022; Views: 3261; Downloads: 33
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4. Vertex-transitive graphs and their arc-typesMarston D. E. Conder, Tomaž Pisanski, Arjana Žitnik, 2017, original scientific article Abstract: Let ▫$X$▫ be a finite vertex-transitive graph of valency ▫$d$▫, and let ▫$A$▫ be the full automorphism group of ▫$X$▫. Then the arc-type of ▫$X$▫ is defined in terms of the sizes of the orbits of the stabiliser ▫$A_v$▫ of a given vertex ▫$v$▫ on the set of arcs incident with ▫$v$▫. Such an orbit is said to be self-paired if it is contained in an orbit ▫$\Delta$▫ of ▫$A$▫ on the set of all arcs of v$X$▫ such that v$\Delta$▫ is closed under arc-reversal. The arc-type of ▫$X$▫ is then the partition of ▫$d$▫ as the sum ▫$n_1 + n_2 + \dots + n_t + (m_1 + m_1) + (m_2 + m_2) + \dots + (m_s + m_s)$▫, where ▫$n_1, n_2, \dots, n_t$▫ are the sizes of the self-paired orbits, and ▫$m_1,m_1, m_2,m_2, \dots, m_s,m_s$▫ are the sizes of the non-self-paired orbits, in descending order. In this paper, we find the arc-types of several families of graphs. Also we show that the arc-type of a Cartesian product of two "relatively prime" graphs is the natural sum of their arc-types. Then using these observations, we show that with the exception of ▫$1+1$▫ and ▫$(1+1)$▫, every partition as defined above is \emph{realisable}, in the sense that there exists at least one vertex-transitive graph with the given partition as its arc-type.
Keywords: symmetry type, vertex-transitive graph, arc-transitive graph, Cayley graph, cartesian product, covering graph
Published in RUP: 03.01.2022; Views: 4212; Downloads: 36
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5. Vpliv prehrane na nivo krvnega sladkorja med telesno aktivnostjo pri bolnikih s sladkorno boleznijo tipa 1 : diplomska nalogaNastja Eler, 2017, undergraduate thesis Keywords: sladkorna bolezen tip 1, prehrana, telesna aktivnost, šport, diabetes type 1, nutrition, physical activity, sport
Published in RUP: 08.06.2018; Views: 9269; Downloads: 8
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6. Imprimitive permutations in primitive groupsJoao Araújo, J. P. Araújo, Peter J. Cameron, Edward Tauscher Dobson, A. Hulpke, P. Lopes, 2017, original scientific article Keywords: primitive groups, imprimitive groups, GAP, permutation type
Published in RUP: 21.02.2018; Views: 5169; Downloads: 263
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7. Roasting intensity of naturally low-caffeine Laurina coffee modulates glucose metabolism and redox balance in humansFilippo Giorgio Di Girolamo, Sara Mazzucco, Roberta Situlin, Nina Mohorko, Zala Jenko Pražnikar, Ana Petelin, Marcello Tence, Rado Pišot, Luciano Navarini, Gianni Biolo, 2016, original scientific article Keywords: coffee, oxidative stress, roasting intensity, Type-2 diabetes mellitus, insulin resistance, omega-3 fatty acids
Published in RUP: 08.08.2016; Views: 6523; Downloads: 152
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9. Reinnervation of Vastus lateralis is increased significantly in seniors (70-years old) with a lifelong history of high-level exerciseSimone Mosole, Katia Rossini, Helmut Kern, Stefan Loefler, Hannah Fruhmann, Michael Vogelauer, Samantha Burggraf, Martina Grim-Stieger, Jan Cvecka, Dušan Hamar, Milan Sedliak, Nejc Šarabon, 2013, original scientific article Keywords: aging, human skelet muscle, lifelong physical exercise, senior sportsmen, denervation and reinnervation, fiber-type grouping, training
Published in RUP: 15.10.2015; Views: 6427; Downloads: 316
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10. Noninvasive estimation of myosin heavy chain composition in human skeletal muscleBoštjan Šimunič, Hans Degens, Joern Rittweger, Marco Vincenzo Narici, Igor B. Mekjavić, Rado Pišot, 2011, original scientific article Keywords: Tensiomyography, fiber type, myosin heavy chain, mechanomyography
Published in RUP: 15.10.2013; Views: 6556; Downloads: 198
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