274 KB14 KB200820252014Anholcer, Marcinštevilka:1letnik:7str. 23-29COBISSID:16792153ISSN:1855-3966URN:URN:NBN:SI:doc-0ZJWJUJUenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneagraph theoryproduct irregularity strengthproduct-irregular labelingteorija grafovtreeProduct irregularity strength of certain graphs|Consider a simple graph ?$G$? with no isolated edges and at most one isolated vertex. A labeling ?$w \colon E(G) \to \{1, 2, \dots,m\}$? is called product - irregular, if all product degrees ?$pdG(v) = \prod_{e \ni v}w(e)$? are distinct. The goal is to obtain a product - irregular labeling that minimizes the maximal label. This minimal value is called the product irregularity strength and denoted ?$ps(G)$?. We give the exact values of ?$ps(G)$? for several families of graphs, as complete bipartite graphs ?$K_{m, n}$?, where ?$2 \le m \le n \le {m + 2 \choose 2}$?, some families of forests, including complete ?$d$?-ary trees, and other graphs with ?$\delta(G) = 1$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije