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2. Distance-transitive graphs admit semiregular automorphismsKlavdija Kutnar, Primož Šparl, 2010, original scientific article Abstract: A distance-transitive graph is a graph in which for every two ordered pairs ofvertices ▫$(u,v)$▫ and ▫$(u',v')$▫ such that the distance between ▫$u$▫ and ▫$v$▫ is equal to the distance between ▫$u'$▫ and ▫$v'$▫ there exists an automorphism of the graph mapping ▫$u$▫ to ▫$u'$▫ and ▫$v$▫ to ▫$v'$▫. A semiregular element of a permutation group is anon-identity element having all cycles of equal length in its cycle decomposition. It is shown that every distance-transitive graph admits a semiregular automorphism. Found in: ključnih besedah Summary of found: ...▫$v'$▫. A semiregular element of a permutation group is anon-identity element having all cycles of... Keywords: distance-transitive graph, vertex-transitive graph, semiregular automorphism, permutation group Published: 15.10.2013; Views: 1755; Downloads: 62 Full text (0,00 KB) |
3. Algebraični aspekti teorije grafovAdemir Hujdurović, 2013, doctoral dissertation Found in: ključnih besedah Summary of found: ...circulant, bicirculant, semiregular automorphism, vertex-transitive graph, half-arc-transitive graph, snark, Cayley... ...action, regular cover of a graph, automorphism group, ... Keywords: 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 Published: 10.07.2015; Views: 1631; Downloads: 7 Full text (0,00 KB) |
4. Minimal normal subgroups of transitive permutation groups of square-free degreeAleksander Malnič, Dragan Marušič, Edward Dobson, 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]). Found in: ključnih besedah Summary of found: ...permutation group of square-free degree contains a semiregular element of prime order, thus giving a... Keywords: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph Published: 03.04.2017; Views: 941; Downloads: 56 Full text (0,00 KB) |
5. Semiregular automorphisms of vertex-transitive graphs of certain valenciesDragan Marušič, Edward Dobson, Aleksander Malnič, 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]). Found in: ključnih besedah Summary of found: ...prime, admitting a transitive action of a ▫$\{2,p\}$▫- group, has a non-identity semiregular automorphism. As a... Keywords: mathematics, graph theory, transitive permutation group, 2-closed group, semiregular automorphism, vertex-transitive graph Published: 03.04.2017; Views: 918; Downloads: 50 Full text (0,00 KB) |
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7. On normality of n-Cayley graphsAdemir Hujdurović, Klavdija Kutnar, Dragan Marušič, 2018, original scientific article Found in: ključnih besedah Summary of found: ...vertex-transitive grapht, Cayley graph, semiregular group, n-Cayley graph, normal n-Cayley graph, Cartesian... Keywords: vertex-transitive grapht, Cayley graph, semiregular group, n-Cayley graph, normal n-Cayley graph, Cartesian product Published: 05.04.2018; Views: 947; Downloads: 95 Full text (0,00 KB) |