295 KB24 KB200820252019Fraser, JayJeans, OliviaŠiran, Jozefletnik:16številka:2str. 403-410ISSN:1855-3966COBISSID_HOST:18793049URN:URN:NBN:SI:doc-K94P6FRJenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaautomorphism groupgrupa avtomorfizmovregular mapregularni zemljevidsebi-dualen zemljevidsebi-Petriejevo-dualen zemljevidself-dual mapself-Petrie-dual mapRegular self-dual and self-Petrie-dual maps of arbitrary valency|The existence of a regular, self-dual and self-Petrie-dual map of any given even valency has been proved by D. Archdeacon et al. Trans. Am. Math. Soc. 366, No. 8, 4491--4512 (2014). In this paper we extend this result to any odd valency ?$\geq 5$?. This is done using algebraic number theory and maps defined on the groups ?$\mathrm{PSL}(2, p)$? in the case of odd prime valency ?$\geq 5$? and valency 9, and using coverings for the remaining odd valenciesObstoj regularnega, sebi-dualnega in sebi-Petriejevo-dualnega zemljevida poljubne sode stopnje so dokazali D. Archdeacon, M. Conder in J. Širáň (2014). V članku razširimo ta rezultat na poljubno liho stopnjo ?$\geq 5$?. To storimo z uporabo algebraične teorije števil in zemljevidov, definiranih na grupah ?$\mathrm{PSL}(2, p)$? v primeru lihe praštevilske stopnje ?$\geq 5$? in valence 9, za ostale lihe stopnje pa z uporabo krovnih preslikavTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije