311 KB24 KB200820252021Cioaba, Sebastian M.Guo, KrystalHaemers, Willem H.številka:2letnik:20str. 187-194DOI:10.26493/1855-3974.2435.ec9ISSN:1855-3966COBISSID_HOST:91633923URN:URN:NBN:SI:doc-ZOBRPAC9enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporanea1-factorization1-faktorizacijabarvanje povezavchromatic indexedge coloringkrepko regularen grafkromatični indeksstrongly regular graphThe chromatic index of strongly regular graphs|We determine (partly by computer search) the chromatic index (edge-chromatic number) of many strongly regular graphs (SRGs), including the SRGs of degree ?$k \leq 18$? and their complements, the Latin square graphs and their complements, and the triangular graphs and their complements. Moreover, using a recent result of Ferber and Jain, we prove that an SRG of even order ?$n$?, which is not the block graph of a Steiner 2-design or its complement, has chromatic index ?$k$?, when ?$n$? is big enough. Except for the Petersen graph, all investigated connected SRGs of even order have chromatic index equal to ?$k$?, i.e., they are class 1, and we conjecture that this is the case for all connected SRGs of even orderDoločimo (deloma s pomočjo računalnika) kromatični indeks (povezavno kromatično število) mnogih krepko regularnih grafov, vključno s krepko regularnimi grafi stopnje ?$k \leq 18$? in njihovimi komplementi, grafi latinskih kvadratov in njihovimi komplementi ter trikotnimi grafi in njihovimi komplementi. Poleg tega, z uporabo nedavnega rezultata Ferberja in Jaina, dokažemo, da ima krepko regularen graf sodega reda ?$n$?, ki ni bločni graf Steinerjevega 2-načrta ali njegovega komplementa, kromatični indeks ?$k$?, če je ?$n$? dovolj velik. Razen za Petersenov graf imajo vsi raziskani povezani krepko regularni grafi sodega reda kromatični indeks enak ?$k$?, kar pomeni, da sodijo v razred 1; postavimo domnevo, da je to res za vse povezane krepko regularne grafe sodega redaTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije