| Title: | Colour-permuting automorphisms of complete Cayley graphs |
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| Authors: | ID Alimirzaei, Shirin (Author)
ID Morris, Dave Witte (Author) |
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| Files: |  ADAM_Alimirzaei,Morris_2025.pdf (453,60 KB)
MD5: A640B318936CC4BE7805700B1070E370
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| 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. |
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| Keywords: | Cayley graph, automorphism, colour-permuting, complete graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 21.02.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 18 str. |
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| Numbering: | Vol. 8, no. 1, [article no.] P1.04 |
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| PID: | 20.500.12556/RUP-22060  |
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| UDC: | 519.17 |
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| eISSN: | 2590-9770 |
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| DOI: | https://doi.org/10.26493/2590-9770.1795.a62 |
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| Publication date in RUP: | 03.11.2025 |
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| Views: | 152 |
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| Downloads: | 1 |
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