20.500.12556/RUP-885 On non-normal arc-transitive 4-valent dihedrants Let ▫$X$▫ be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group ▫$D_n$▫ such that ▫$X$▫ is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within ▫$D_n$▫. It is shown that ▫$X$▫ is isomorphic either to the lexicographic product ▫$C_n[2K_1]$▫ with ▫$n \geq 4$▫ even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively. Naj bo ▫$X$▫ povezan nenormalen 4-valenten ločno-tranzitiven Cayleyev graf diedrske grupe ▫$D_n$▫, tako da je ▫$X$▫ dvodelen in ustrezna biparticija vozlišč ustreza dvema orbitama ciklične podgrupe znotraj ▫$D_n$▫. Dokazano je, da je tedaj ▫$X$▫ izomorfen bodisi leksikografskemu produktu ▫$C_n[2K_1]$▫ za ▫$n \geq 4$▫ sodo, bodisi enemu od petih posebnih grafov na 10, 14, 26, 28 oz. 30 vozliščih. Cayley graph arc transitivity dihedral group Cayleyjev graf ločna tranzitivnost diedrska grupa true true false Angleški jezik Angleški jezik Delo ni kategorizirano 2013-10-15 12:05:18 2013-10-15 12:05:18 2024-03-01 11:59:14 0000-00-00 00:00:00 2010 0 0 str. 1485-1498 no. 8 Vol. 26 2010 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1439-8516 519.17 1024270932 http://www.springerlink.com/content/91474375p0273m92/fulltext.pdf 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=885 Inštitut Andrej Marušič 0 0 0