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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: 1973; 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.
34.
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: 2176; Prenosov: 100
.pdf Celotno besedilo (281,25 KB)

35.
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: 1643; Prenosov: 22
URL Povezava na celotno besedilo

36.
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: 2140; Prenosov: 18
URL Povezava na celotno besedilo

37.
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: 1705; Prenosov: 25
URL Povezava na celotno besedilo

38.
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: 2340; Prenosov: 89
URL Povezava na celotno besedilo

39.
Symmetry structure of bicirculants
Aleksander Malnič, Dragan Marušič, Primož Šparl, Boštjan Frelih, 2007, izvirni znanstveni članek

Opis: An ▫$n$▫-bicirculant is a graph having an automorphism with two orbits of length ▫$n$▫ and no other orbits. Symmetry properties of ▫$p$▫-bicirculants, ▫$p$▫ a prime, are extensively studied. In particular, the actions of their automorphism groups are described in detail in terms of certain algebraic representation of such graphs.
Ključne besede: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Objavljeno v RUP: 03.04.2017; Ogledov: 2445; Prenosov: 95
URL Povezava na celotno besedilo

40.
On strongly regular bicirculants
Aleksander Malnič, Dragan Marušič, Primož Šparl, 2007, izvirni znanstveni članek

Opis: An ▫$n$▫-bicirculantis a graph having an automorphism with two orbits of length ▫$n$▫ and no other orbits. This article deals with strongly regular bicirculants. It is known that for a nontrivial strongly regular ▫$n$▫-bicirculant, ▫$n$▫ odd, there exists a positive integer m such that ▫$n=2m^2+2m+1▫$. Only three nontrivial examples have been known previously, namely, for ▫$m=1,2$▫ and 4. Case ▫$m=1$▫ gives rise to the Petersen graph and its complement, while the graphs arising from cases ▫$m=2$▫ and ▫$m=4$▫ are associated with certain Steiner systems. Similarly, if ▫$n$▫ is even, then ▫$n=2m^2$▫ for some ▫$m \ge 2$▫. Apart from a pair of complementary strongly regular 8-bicirculants, no other example seems to be known. A necessary condition for the existence of a strongly regular vertex-transitive ▫$p$▫-bicirculant, ▫$p$▫ a prime, is obtained here. In addition, three new strongly regular bicirculants having 50, 82 and 122 vertices corresponding, respectively, to ▫$m=3,4$▫ and 5 above, are presented. These graphs are not associated with any Steiner system, and together with their complements form the first known pairs of complementary strongly regular bicirculants which are vertex-transitive but not edge-transitive.
Ključne besede: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Objavljeno v RUP: 03.04.2017; Ogledov: 3303; Prenosov: 88
URL Povezava na celotno besedilo

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