1. 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: 378; Prenosov: 3
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4. Cyclic m-DCI-groups and m-CI-groupsIstván Kovács, Luka Šinkovec, 2025, izvirni znanstveni članek Opis: Based on the earlier work of Li from 1997 and Dobson from 2008, in this paper we complete the classification of cyclic m-DCI-groups and m-CI-groups. For a positive integer m such that m ≥ 3, we show that the group ℤ_(n) is an m-DCI-group if and only if n is not divisible by 8 nor by p² for any odd prime p < m. Furthermore, if m ≥ 6, then we show that ℤn is an m-CI-group if and only if either n ∈ {8, 9, 18}, or n ∉ {8, 9, 18} and n is not divisible by 8 nor by p² for any odd prime p < (m - 1)/2.
Ključne besede: Cayley graph, cyclic group, m-CI-group, m-DCI-group
Objavljeno v RUP: 01.04.2025; Ogledov: 1063; Prenosov: 12
Celotno besedilo (446,08 KB)
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5. Partial geometries with regular automorphism groups : master’s thesisAdisa Hodžić, 2024, magistrsko delo Ključne besede: (near-) linear space, projective plane, affine plane, partial geometry, generalized quadrangle, strongly regular graph, partial difference set, automorphism group
Objavljeno v RUP: 25.12.2024; Ogledov: 1872; Prenosov: 31
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6. Posplošitev Lijeve domneve in popolna klasifikacija cikličnih m-(D)CI-grup : magistrsko deloLuka Šinkovec, 2023, magistrsko delo Ključne besede: (un)directed Cayley graph, cyclic group, (un)directed circulant graph, Cayley isomorphism, (un)directed CI-graph, (D)CI-group, m-(D)CI-group, key, generalised multiplier
Objavljeno v RUP: 11.09.2023; Ogledov: 2036; Prenosov: 30
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8. The automorphism groups of non-edge transitive rose window graphsEdward Tauscher Dobson, István Kovács, Štefko Miklavič, 2015, izvirni znanstveni članek Opis: In this paper, we determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we determine the isomorphism classes of non-edge-transitive rose window graphs.
Ključne besede: rose window graphs, automorphism group, isomorphism problem, vertex-transitive graph
Objavljeno v RUP: 31.12.2021; Ogledov: 2562; Prenosov: 43
Celotno besedilo (275,74 KB) |
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