1. Families of association schemes on triples from two-transitive groupsJose Maria P. Balmaceda, Dom Vito A. Briones, 2025, izvirni znanstveni članek Opis: Association schemes on triples (ASTs) are ternary analogues of classical association schemes. Similar to how Schurian association schemes arise from transitive groups, ASTs arise from two-transitive groups. In this paper, we obtain the third valencies and the number of relations of the ASTs obtained from two-transitive permutation groups. Further, we obtain the intersection numbers of the ASTs produced by PΓL(k, n), PSL(2, n), AΓL(k, n), and the sporadic two-transitive groups. In particular, the ASTs from the actions of PΓL(k, n), PSL(2, n), and the sporadic groups are commutative.
Ključne besede: association scheme on triples, permutation group, ternary algebra, algebraic combinatorics
Objavljeno v RUP: 21.10.2025; Ogledov: 689; Prenosov: 10
 Celotno besedilo (417,07 KB) |
2. Edge-transitive core-free Nest graphsIstván Kovács, 2025, izvirni znanstveni članek Opis: A finite simple graph Γ is called a Nest graph if it is regular of valency 6 and admits an automorphism ρ with two orbits of the same length such that at least one of the subgraphs induced by these orbits is a cycle. We say that Γ is core-free if no non-trivial subgroup of the group generated by ρ is normal in Aut(Γ). In this paper, we show that, if Γ is edge-transitive and core-free, then it is isomorphic to one of the following graphs: the complement of the Petersen graph, the Hamming graph H(2,4), the Shrikhande graph and a certain normal 2-cover of K_{3,3} by ℤ_2^4.
Ključne besede: bicirculant, edge-transitive, primitive permutation group
Objavljeno v RUP: 10.09.2025; Ogledov: 727; Prenosov: 6
Celotno besedilo (466,20 KB) |
3. Odd extensions of transitive groups via symmetric graphs - The cubic caseKlavdija Kutnar, Dragan Marušič, 2018, izvirni znanstveni članek Opis: When dealing with symmetry properties of mathematical objects, one of the fundamental questions is to determine their full automorphism group. In this paper this question is considered in the context of even/odd permutations dichotomy. More precisely: when is it that the existence of automorphisms acting as even permutations on the vertex set of a graph, called even automorphisms, forces the existence of automorphisms that act as odd permutations, called odd automorphisms. As a first step towards resolving the above question, complete information on the existence of odd automorphisms in cubic symmetric graphs is given.
Ključne besede: automorphism group, arc-transitive, even permutation, odd permutation, cubic symmetric graph
Objavljeno v RUP: 19.11.2018; Ogledov: 4304; Prenosov: 213
 Povezava na celotno besedilo |
4. Odd automorphisms in vertex-transitive graphsAdemir 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: 4258; Prenosov: 105
Celotno besedilo (281,25 KB) |
5. |
6. Minimal normal subgroups of transitive permutation groups of square-free degreeEdward Tauscher 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: 4416; Prenosov: 102
Povezava na celotno besedilo |
7. Semiregular automorphisms of vertex-transitive graphs of certain valenciesEdward Tauscher 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: 4307; Prenosov: 104
Povezava na celotno besedilo |
8. |
9. Decomposition of skew-morphisms of cyclic groupsIstván Kovács, Roman Nedela, 2011, izvirni znanstveni članek Opis: A skew-morphism of a group ▫$H$▫ is a permutation ▫$\sigma$▫ of its elements fixing the identity such that for every ▫$x, y \in H$▫ there exists an integer ▫$k$▫ such that ▫$\sigma (xy) = \sigma (x)\sigma k(y)$▫. It follows that group automorphisms are particular skew-morphisms. Skew-morphisms appear naturally in investigations of maps on surfaces with high degree of symmetry, namely, they are closely related to regular Cayley maps and to regular embeddings of the complete bipartite graphs. The aim of this paper is to investigate skew-morphisms of cyclic groups in the context of the associated Schur rings. We prove the following decomposition theorem about skew-morphisms of cyclic groups ▫$\mathbb Z_n$▫: if ▫$n = n_{1}n_{2}$▫ such that ▫$(n_{1}n_{2}) = 1$▫, and ▫$(n_{1}, \varphi (n_{2})) = (\varphi (n_{1}), n_{2}) = 1$▫ (▫$\varphi$▫ denotes Euler's function) then all skew-morphisms ▫$\sigma$▫ of ▫$\mathbb Z_n$▫ are obtained as ▫$\sigma = \sigma_1 \times \sigma_2$▫, where ▫$\sigma_i$▫ are skew-morphisms of ▫$\mathbb Z_{n_i}, \; i = 1, 2$▫. As a consequence we obtain the following result: All skew-morphisms of ▫$\mathbb Z_n$▫ are automorphisms of ▫$\mathbb Z_n$▫ if and only if ▫$n = 4$▫ or ▫$(n, \varphi(n)) = 1$▫.
Ključne besede: cyclic group, permutation group, skew-morphism, Schur ring
Objavljeno v RUP: 15.10.2013; Ogledov: 6613; Prenosov: 114
Povezava na celotno besedilo |
10. |
