1. 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: 02.01.2022; Views: 1411; Downloads: 21
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6. Strategies for improvement of visibility and acceptance of modified woodAnna Malgorzata Sandak, Viviana Golja, Julia Belda, Jens Geissmann-Fuchs, Kelly Peeters, Jakub Michal Sandak, Janja Juhant Grkman, Silvo Hribernik, Dean Lipovac, Peter Nadrah, 2018, published scientific conference contribution abstract Keywords: modified wood, interaction with materials, human perception, product visibility
Published in RUP: 17.12.2018; Views: 2891; Downloads: 79
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9. Life cycle assessment - opportunities for forest products sectorAndreja Kutnar, Callum A. S. Hill, 2017, original scientific article Keywords: environmental impact, environmental product declaration (EPD), forest products, life cycle assessment (LCA), O-LCA, product category rules (PCR), S-LCA, wood
Published in RUP: 15.11.2017; Views: 4159; Downloads: 94
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10. Characterizations of minimal dominating sets and the well-dominated property in lexicographic product graphsDidem Gozüpek, Ademir Hujdurović, Martin Milanič, 2017, original scientific article Keywords: lekisikografski product grafov, minimalna dominantna množica, dobro dominiran graf, nesvodljiva dominantna množica, lexicographic product of graphs, minimal dominating set, well-dominated graph, irreducible dominating set
Published in RUP: 14.11.2017; Views: 2687; Downloads: 66
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