20.500.12556/RUP-17619 On colour-preserving automorphisms of Cayley graphs O barve-ohranjajočih avtomorfizmih Cayleyjevih grafov 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. Študiramo avtomorfizme Cayleyjevega grafa, ki ohranjajo njegovo naravno barvanje povezav. Natančneje, zanimajo nas takšne grupe ▫$G$▫, pri katerih ima vsak tak avtomorfizem vsakega povezanega Cayleyjevega grafa na grupi ▫$G$▫ zelo enostavno obliko: je kompozitum leve translacije in avtomorfizma grupe. Najdemo razrede grup, ki imajo to lastnost, in določimo rede vseh grup, ki nimajo te lastnosti. Imamo tudi analogne rezultate za avtomorfizme, ki barv ne ohranjajo, ampak jih permutirajo. Cayley graph automorphism colour-preserving colour-permuting Cayleyjev graf avtomorfizem barve-ohranjajoč barve-permutirajoč true true false Angleški jezik Slovenski jezik Neznano 2022-01-03 00:36:39 2022-01-03 00:36:41 2024-03-01 14:39:20 0000-00-00 00:00:00 2016 0 0 str. 189-213 no. 1 Vol. 11 2016 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 1855-3966 1537938884 RAZ_Hujdurovic_Ademir_i2016.pdf RAZ_Hujdurovic_Ademir_i2016.pdf 1 7070A1854D320F8AF9555891EA52861F 44e1dae9c85d45b4558cb3fa2778f1ff25a400016caebe7ad17dd208c443048d 77c2a808-c3d6-11ed-b5df-005056bf369b https://repozitorij.upr.si/Dokument.php?lang=slv&id=25936 Založba Univerze na Primorskem 0 0 0