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33. 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: 2303; Downloads: 100
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37. Minimal normal subgroups of transitive permutation groups of square-free degreeEdward Dobson, Aleksander Malnič, Dragan Marušič, Lewis A. Nowitz, 2007, original scientific article Abstract: It is shown that a minimal normal subgroup of a transitive permutation group of square-free degree in its induced action is simple and quasiprimitive, with three exceptions related to ▫$A_5$▫, ▫$A_7$▫, and PSL(2,29). Moreover, it is shown that a minimal normal subgroup of a 2-closed permutation group of square-free degree in its induced action is simple. As an almost immediate consequence, it follows that a 2-closed transitive permutation group of square-free degree contains a semiregular element of prime order, thus giving a partial affirmative answer to the conjecture 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]).
Keywords: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph
Published in RUP: 03.04.2017; Views: 2433; Downloads: 89
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38. Semiregular automorphisms of vertex-transitive graphs of certain valenciesEdward Dobson, Aleksander Malnič, Dragan Marušič, Lewis A. Nowitz, 2007, original scientific article Abstract: 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]).
Keywords: mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph
Published in RUP: 03.04.2017; Views: 2483; Downloads: 83
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39. Določeni razredi (hiper)grafov in njihove algebraične lastnosti : doktorska disertacijaPaweł Petecki, 2016, doctoral dissertation Keywords: hypergraph, hamiltonian cycle, decomposition, double generalized Petersen graph, automorphism group, vertex-transitive, sign graph, L-eigenvalue, lollipop graph
Published in RUP: 09.08.2016; Views: 3175; Downloads: 30
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