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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: 390; Prenosov: 10
 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: 1163; Prenosov: 15
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7. 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: 1391; Prenosov: 21
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9. Linking rings structures and semisymmetric graphs : combinatorial constructionsPrimož Potočnik, Steve Wilson, 2018, izvirni znanstveni članek Ključne besede: graphs, automorphism group, symmetry, locally arc-transitive graphs, symmetric graphs, cycle structure, linking ring structure
Objavljeno v RUP: 03.01.2022; Ogledov: 1759; Prenosov: 19
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10. Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphismsDragan Marušič, 2017, izvirni znanstveni članek Opis: 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.
Ključne besede: solvable group, semiregular automorphism, fixed-point-free automorphism, polycirculant conjecture
Objavljeno v RUP: 03.01.2022; Ogledov: 1645; Prenosov: 19
Celotno besedilo (235,26 KB) |
