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31.
Vertex-transitive odd numbers
Klavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2017, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: odd automorphism, even-closed, vertex-transitive, graph
Objavljeno v RUP: 15.11.2017; Ogledov: 1711; Prenosov: 25
URL Povezava na celotno besedilo

32.
Minimal normal subgroups of transitive permutation groups of square-free degree
Edward Dobson, Aleksander Malnič, Dragan Marušič, Lewis A. Nowitz, 2007, izvirni znanstveni članek

Opis: 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]).
Ključne besede: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph
Objavljeno v RUP: 03.04.2017; Ogledov: 2342; Prenosov: 89
URL Povezava na celotno besedilo

33.
Semiregular automorphisms of vertex-transitive graphs of certain valencies
Edward 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: 2407; Prenosov: 83
URL Povezava na celotno besedilo

34.
35.
Symmetry of graphs via even/odd automorphisms
Dragan Marušič, Klavdija Kutnar, 2016, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: vertex-transitive, graph, odd automorphism, automorphism group
Objavljeno v RUP: 08.08.2016; Ogledov: 2087; Prenosov: 26
URL Povezava na celotno besedilo

36.
Odd automorphism in vertex-transitive graphs
Klavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2016, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: vertex-transitive, graph, odd automorphism, even-closed
Objavljeno v RUP: 08.08.2016; Ogledov: 2396; Prenosov: 14
URL Povezava na celotno besedilo

37.
Vertex-transitive graphs : why semiregularity matters
Dragan Marušič, 2016, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: vertex-transitive, graph, semiregular
Objavljeno v RUP: 08.08.2016; Ogledov: 2255; Prenosov: 29
URL Povezava na celotno besedilo

38.
39.
Distance-transitive graphs admit semiregular automorphisms
Klavdija Kutnar, Primož Šparl, 2010, izvirni znanstveni članek

Opis: 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.
Ključne besede: distance-transitive graph, vertex-transitive graph, semiregular automorphism, permutation group
Objavljeno v RUP: 15.10.2013; Ogledov: 3282; Prenosov: 98
URL Povezava na celotno besedilo

40.
On cubic non-Cayley vertex-transitive graphs
Klavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, izvirni znanstveni članek

Ključne besede: vertex-transitive graph, non-Cayley graph, automorphism group
Objavljeno v RUP: 15.10.2013; Ogledov: 2861; Prenosov: 129
URL Povezava na celotno besedilo

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