11. Semiregular automorphisms of vertex-transitive graphs of certain valenciesEdward Dobson, Aleksander Malnič, Dragan Marušič, Lewis A. Nowitz, 2007, izvirni znanstveni članek Opis: It is shown that a vertex-transitive graph of valency ▫$p+1$▫, ▫$p$▫ a prime, admitting a transitive action of a ▫$\{2,p\}$▫-group, has a non-identity semiregular automorphism. As a consequence, it is proved that a quartic vertex-transitive graph has a non-identity semiregular automorphism, thus giving a partial affirmative answer to the conjecture that all vertex-transitive graphs have such an automorphism and, more generally, that all 2-closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs, Discrete Math. 36 (1981) 69-81; P.J. Cameron (Ed.), Problems from the Fifteenth British Combinatorial Conference, Discrete Math. 167/168 (1997) 605-615]).
Ključne besede: mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph
Objavljeno v RUP: 03.04.2017; Ogledov: 2488; Prenosov: 83
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13. Algebraični aspekti teorije grafov : doktorska disertacijaAdemir Hujdurović, 2013, doktorska disertacija Ključne besede: circulant, bicirculant, semiregular automorphism, vertex-transitive graph, half-arc-transitive graph, snark, Cayley graph, quasi m-Cayley graph, generalized Cayley graph, I-regular action, regular cover of a graph, automorphism group
Objavljeno v RUP: 10.07.2015; Ogledov: 3480; Prenosov: 42
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17. Recent trends and future directions in vertex-transitive graphsKlavdija Kutnar, Dragan Marušič, 2008, izvirni znanstveni članek Opis: A graph is said to be vertex-transitive if its automorphism group acts transitively on the vertex set. Some recent developments and possible future directions regarding two famous open problems, asking about existence of Hamilton paths and existence of semiregular automorphisms in vertex-transitive graphs, are discussed, together with some recent results on arc-transitive graphs and half-arc-transitive graphs, two special classes of vertex-transitive graphs that have received particular attention over the last decade.
Ključne besede: vertex-transitive graph, arc-transitive graph, half-arc-transitive graph, Hamilton cycle, Hamilton path, semiregular group, (im)primitive group
Objavljeno v RUP: 15.10.2013; Ogledov: 3183; Prenosov: 132
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