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1.
Classification of cubic vertex-transitive tricirculants
Primož Potočnik, Micael Toledo, 2020, original scientific article

Keywords: graph, cubic, semiregular automorphism, tricirculant, vertex-transitive
Published in RUP: 03.01.2022; Views: 795; Downloads: 40
.pdf Full text (1,18 MB)

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Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphisms
Dragan 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: 763; Downloads: 17
.pdf Full text (235,26 KB)

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On colour-preserving automorphisms of Cayley graphs
Ademir Hujdurović, Klavdija Kutnar, Dave Witte Morris, Joy Morris, 2016, original scientific article

Abstract: We study the automorphisms of a Cayley graph that preserve its natural edge-colouring. More precisely, we are interested in groups ▫$G$▫, such that every such automorphism of every connected Cayley graph on ▫$G$▫ has a very simple form: the composition of a left-translation and a group automorphism. We find classes of groups that have the property, and we determine the orders of all groups that do not have the property. We also have analogous results for automorphisms that permute the colours, rather than preserving them.
Keywords: Cayley graph, automorphism, colour-preserving, colour-permuting
Published in RUP: 03.01.2022; Views: 652; Downloads: 16
.pdf Full text (412,93 KB)

5.
The automorphism groups of non-edge transitive rose window graphs
Edward 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: 865; Downloads: 18
.pdf Full text (275,74 KB)

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A family of non-Cayley cores that are constructed from vertex-transitive or strongly regular self-complementary graphs
Marko Orel, 2021, published scientific conference contribution abstract

Keywords: cores, graph homomorphisms, automorphism group, self-complementary graphs
Published in RUP: 30.07.2021; Views: 963; Downloads: 73
URL Link to full text
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9.
A family of non-Cayley cores that are constructed from vertex-transitive or strongly regular self-complementary graphs
Marko Orel, 2021, published scientific conference contribution abstract

Keywords: cores, graph homomorphisms, automorphism group, self-complementary graphs
Published in RUP: 30.07.2021; Views: 1166; Downloads: 42
.pdf Full text (1,01 MB)
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