383 KB58 KB200820252019Dam, Edwin Robert vanJazaeri, Mojtabaštevilka:1letnik:17str. 203-222ISSN:1855-3966COBISSID_HOST:18954073URN:URN:NBN:SI:doc-E7LFDSTNenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaCayley graphCayleyjev grafdistance-regular graphrazdaljno-regularen grafDistance-regular Cayley graphs with small valency|We consider the problem of which distance-regular graphs with small valency are Cayley graphs. We determine the distance-regular Cayley graphs with valency at most 4, the Cayley graphs among the distance-regular graphs with known putative intersection arrays for valency 5, and the Cayley graphs among all distance-regular graphs with girth 3 and valency 6 or 7. We obtain that the incidence graphs of Desarguesian affine planes minus a parallel class of lines are Cayley graphs. We show that the incidence graphs of the known generalized hexagons are not Cayley graphs, and neither are some other distance-regular graphs that come from small generalized quadrangles or hexagons. Among some ''exceptional'' distance-regular graphs with small valency, we find that the Armanios-Wells graph and the Klein graph are Cayley graphsProblem, ki ga obravnavamo, sprašuje, kateri razdaljno-regularni grafi z majhno valenco so Cayleyjevi grafi. Poišcemo Cayleyjeve grafe med razdaljno-regularnimi grafi z valenco kvecjemu 4, med razdaljno-regularnimi grafi za znane domnevne presečne tabele z valenco 5 in med vsemi razdaljno-regularnimi grafi z ožino 3 in valenco 6 ali 7. Ugotovimo, da so incidenčni grafi Desarguesovih afinih ravnin brez enega razreda vzporednih premic Cayleyjevi grafi. Pokažemo, da incidenčni grafi znanih posplošenih šestkotnikov niso Cayleyjevi grafi; prav tako niso Cayleyjevi nekateri drugi razdaljno-regularni grafi, ki izhajajo iz majhnih posplošenih štirikotnikov ali šestkotnikov. Med ''izjemnimi'' razdaljno-regularnimi grafi z majhno valenco smo našli dva, ki sta Cayleyjeva, in sicer sta to Armanios-Wellsov graf in Kleinov grafTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije