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2. Cyclic m-DCI-groups and m-CI-groupsIstván Kovács, Luka Šinkovec, 2025, original scientific article Abstract: 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.
Keywords: Cayley graph, cyclic group, m-CI-group, m-DCI-group
Published in RUP: 01.04.2025; Views: 354; Downloads: 10
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3. Partial geometries with regular automorphism groups : master’s thesisAdisa Hodžić, 2024, master's thesis Keywords: (near-) linear space, projective plane, affine plane, partial geometry, generalized quadrangle, strongly regular graph, partial difference set, automorphism group
Published in RUP: 25.12.2024; Views: 1129; Downloads: 15
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5. Posplošitev Lijeve domneve in popolna klasifikacija cikličnih m-(D)CI-grup : magistrsko deloLuka Šinkovec, 2023, master's thesis Keywords: (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
Published in RUP: 11.09.2023; Views: 1346; Downloads: 21
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7. Linking rings structures and semisymmetric graphs : combinatorial constructionsPrimož Potočnik, Steve Wilson, 2018, original scientific article Keywords: graphs, automorphism group, symmetry, locally arc-transitive graphs, symmetric graphs, cycle structure, linking ring structure
Published in RUP: 03.01.2022; Views: 1730; Downloads: 19
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8. Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphismsDragan Marušič, 2017, original scientific article Abstract: It has been conjectured that automorphism groups of vertex-transitive (di)graphs, and more generally 2-closures of transitive permutation groups, must necessarily possess a fixed-point-free element of prime order, and thus a non-identity element with all orbits of the same length, in other words, a semiregular element. The known affirmative answers for graphs with primitive and quasiprimitive groups of automorphisms suggest that solvable groups need to be considered if one is to hope for a complete solution of this conjecture. It is the purpose of this paper to present an overview of known results and suggest possible further lines of research towards a complete solution of the problem.
Keywords: solvable group, semiregular automorphism, fixed-point-free automorphism, polycirculant conjecture
Published in RUP: 03.01.2022; Views: 1619; Downloads: 19
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9. Testing whether the lifted group splitsRok Požar, 2016, original scientific article Abstract: Let a group of automorphisms lift along a regular covering projection of connected graphs given combinatorially by means of voltages. The data that determine the lifted group and its action are then conveniently encoded in terms of voltages as well. Along these lines, an algorithm for testing whether the lifted group is a split extension of the group of covering transformations has recently been proposed in the case when the group of covering transformations is solvable. It consists of decomposing the covering into a series of coverings with elementary abelian groups of covering transformations, and inductively solving the problem at every elementary abelian step. Although the explicit construction of the lifted group is not needed, it still involves time and space consuming constructions of certain subgroups in the lifted group at every step except at the final one. In this paper, an improved version that completely avoids such constructions is presented. From voltage distribution we first compute the weak action and the factor set that determine the lifted group, and we then carry out the test by extracting the necessary information only from the corresponding weak actions and factor sets at every step. An experimental comparison is made against the previous version.
Keywords: algorithm, graph, group extension, lifting automorphisms, regular covering projection, voltages
Published in RUP: 03.01.2022; Views: 1644; Downloads: 24
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10. The automorphism groups of non-edge transitive rose window graphsEdward Dobson, István Kovács, Štefko Miklavič, 2015, original scientific article Abstract: 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.
Keywords: rose window graphs, automorphism group, isomorphism problem, vertex-transitive graph
Published in RUP: 31.12.2021; Views: 1858; Downloads: 26
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