415 KB58 KB200820252014Bhoumik, SoumyaDobson, EdwardMorris, Joyštevilka:2letnik:7str. 499-518COBISSID:17165145ISSN:1855-3966URN:URN:NBN:SI:doc-EOQHLR3SenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneaautomorphism groupCayley graphcirculant graphDRRgrafiGRRgrupeOn the automorphism groups of almost all circulant graphs and digraphs|We attempt to determine the structure of the automorphism group of a generic circulant graph. We first show that almost all circulant graphs have automorphism groups as small as possible. The second author has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism group is not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose order is in a "large" subset of integers. We note that all non-normal circulant (di)graphs can be classified into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraphTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije