528 KB76 KB200820252021Zhang, Mi-MiZhou, Jin-Xinštevilka:2letnik:21str. 175-200DOI:10.26493/1855-3974.2373.c02COBISSID_HOST:112328963ISSN:1855-3966URN:URN:NBN:SI:doc-QQZRSKJJenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneabi-Cayleybi-Cayleyjevbi-diedrski grafbi-dihedrantCayley graphCayleyjev grafdiedrska grupadiedrski grafdihedral groupdihedrantne-Cayleyjevnon-CayleyTrivalent dihedrants and bi-dihedrants|A Cayley (resp. bi-Cayley) graph on a dihedral group is called a dihedrant (resp. bi-dihedrant). In 2000, a classification of trivalent arc-transitive dihedrants was given by D. Marušič and T. Pisanski "Symmetries of hexagonal molecular graphs on the torus", Croat. Chem. Acta 73, No. 4, 969-981 (2000), https://hrcak.srce.hr/131972 and several years later, trivalent non-arc-transitive dihedrants of order ?$4p$? or ?$8p$? (?$p$? a prime) were classified by Feng et al. As a generalization of these results, our first result presents a classification of trivalent non-arc-transitive dihedrants. Using this, a complete classification of trivalent vertex-transitive non-Cayley bi-dihedrants is given, thus completing the study of trivalent bi-dihedrants initiated in our previous paper Discrete Math. 340, No. 8, 1757-1772 (2017). As a by-product, we generalize a theorem in The Electron. J. Comb. 19, No. 1, Research Paper P53, 13 p. (2012)Cayleyjev (oz. bi-Cayleyjev) graf diedrske grupe se imenuje diedrski (oz. bi-diedrski graf). Leta 2000 sta Marušič in Pisanski predstavila klasifikacijo trivalentnih ločno-tranzitivnih diedrskih grafov, nekaj let kasneje pa so Feng in dr. klasificirali tiste trivalentne diedrske grafe reda ?$4p$? ali ?$8p$? (kjer je ?$p$? praštevilo), ki niso ločno tranzitivni. V tem članku posplošiva te rezultate; najprej predstaviva klasifikacijo tistih trivalentnih diedrskih grafov, ki niso ločno tranzitivni. Na tej osnovi podava popolno klasifikacijo trivalentnih točkovno tranzitivnih ne-Cayleyjevih bi-diedrskih grafov, s čimer zaključiva raziskavo trivalentnih bi-diedrskih grafov, ki sva jo začela v najinem prejšnjem članku Discrete Math. 340 (2017) 1757-1772. Poleg tega posplošiva še izrek iz The Electron. J. Comb. 19, No. 1, Research Paper P53, 13 p. (2012)TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije