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31.
Symmetric graphs: why semiregularity matters
Dragan Marušič, 2018, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: vertex-transitive graph, semiregular automorphism, elusive group, solvable group
Objavljeno v RUP: 07.02.2018; Ogledov: 1974; Prenosov: 28
URL Povezava na celotno besedilo

32.
Graphs with large minimal vertex-transitive automorphism groups
Robert Jajcay, 2018, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: vertex-transitive graph, automorphism group, symmetric graph
Objavljeno v RUP: 07.02.2018; Ogledov: 1792; Prenosov: 30
URL Povezava na celotno besedilo

33.
Odd automorphisms in vertex-transitive graphs
Ademir Hujdurović, Klavdija Kutnar, Dragan Marušič, 2016, izvirni znanstveni članek

Opis: 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.
Ključne besede: graph, vertex-transitive, automorphism group, even permutation, odd permutation
Objavljeno v RUP: 15.11.2017; Ogledov: 2177; Prenosov: 100
.pdf Celotno besedilo (281,25 KB)

34.
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: 1645; Prenosov: 22
URL Povezava na celotno besedilo

35.
Symmetric graphs: why semiregularity matters
Dragan Marušič, 2017, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: vertex-transitive, graph, semiregular automorphism
Objavljeno v RUP: 15.11.2017; Ogledov: 2154; Prenosov: 18
URL Povezava na celotno besedilo

36.
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: 1708; Prenosov: 25
URL Povezava na celotno besedilo

37.
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: 2341; Prenosov: 89
URL Povezava na celotno besedilo

38.
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

39.
40.
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: 2085; Prenosov: 26
URL Povezava na celotno besedilo

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