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Colour-permuting automorphisms of complete Cayley graphs
Shirin Alimirzaei, Dave Witte Morris, 2025, original scientific article

Abstract: Let G be a (finite or infinite) group, and let KG = Cay(G; G \ {1}) be the complete graph with vertex set G, considered as a Cayley graph of G. Being a Cayley graph, it has a natural edge-colouring by sets of the form {s, s-1} for s in G. We prove that every colour-permuting automorphism of KG is an affine map, unless G is isomoprhic to the direct product of Q8 and B, where Q8 is the quaternion group of order 8, and B is an abelian group, such that b2 is trivial for all b in B. We also prove (without any restriction on G) that every colour-permuting automorphism of KG is the composition of a group automorphism and a colour-preserving graph automorphism. This was conjectured by D. P. Byrne, M. J. Donner, and T. Q. Sibley in 2013.
Keywords: Cayley graph, automorphism, colour-permuting, complete graphs
Published in RUP: 03.11.2025; Views: 559; Downloads: 4
Full text (453,60 KB)

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: 2671; Downloads: 43
Full text (412,93 KB)

Chemical and appearance changes of wood due to artificial weathering - dose-response model
Marta Petrillo, Jakub Michal Sandak, Paolo Grossi, Anna Malgorzata Sandak, 2019, original scientific article

Keywords: wood weathering, dose-response model, multi-sensor measurement, near infrared, colour, gloss
Published in RUP: 13.02.2019; Views: 4917; Downloads: 184
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