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72. Odd automorphisms in vertex-transitive graphsAdemir Hujdurović, Klavdija Kutnar, Dragan Marušič, 2016, original scientific article Abstract: An automorphism of a graph is said to be even/odd if it acts on the set of vertices as an even/odd permutation. In this article we pose the problem of determining which vertex-transitive graphs admit odd automorphisms. Partial results for certain classes of vertex-transitive graphs, in particular for Cayley graphs, are given. As a consequence, a characterization of arc-transitive circulants without odd automorphisms is obtained. Keywords: graph, vertex-transitive, automorphism group, even permutation, odd permutation Published in RUP: 15.11.2017; Views: 2393; Downloads: 100 Full text (281,25 KB) |
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78. Osnovne lastnosti hipergrup : magistrsko deloMojca Pev, 2017, master's thesis Keywords: hiperoperacija, polhipergrupa, podhipergrupa, hipergrupa, asociativnost, aksiom reprodukcije, homomorfizem hipergrupe, regularna in močno regularna relacija, popolna hipergrupa, pridružitveni prostor, kanonična hipergrupa Published in RUP: 09.11.2017; Views: 2472; Downloads: 78 Link to full text This document has more files! More... |
79. On cyclic edge-connectivity of fullerenesKlavdija Kutnar, Dragan Marušič, 2008, original scientific article Abstract: A graph is said to be cyclically ▫$k$▫-edge-connected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single ▫$k$▫-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/20-1/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫. Keywords: graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matching Published in RUP: 03.04.2017; Views: 2241; Downloads: 138 Link to full text |
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