0 KB248 KB27 KB200820252013Klotz, WalterSander, Torstenštevilka:2letnik:6str. 289-299COBISSID:16475225ISSN:1855-3966URN:URN:NBN:SI:doc-RHVX49XZenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneaCayley graphsgraph productsintegral graphsteorija grafovGCD-graphs and NEPS of complete graphs|A gcd-graph is a Cayley graph over a finite abelian group defined by greatest common divisors. Such graphs are known to have integral spectrum. A non-complete extended ?$p$?-sum, or NEPS in short, is well-known general graph product. We show that the class of gcd-graphs and the class of NEPS of complete graphs coincide. Thus, a relation between the algebraically defined Cayley graphs and the combinatorially defined NEPS of complete graphs is established. We use this link to show that gcd-graphs have a particularly simple eigenspace structure, to be precise, that every eigenspace of the adjacency matrix of a gcd-graph has a basis with entries ?$-1,0,1$? onlyTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije