20.500.12556/DKUM-52006 Some Steiner concepts on lexicographic products of graphs The smallest tree that contains all vertices of a subset ▫$W$▫ of ▫$V(G)$▫ is called a Steiner tree. The number of edges of such a tree is the Steiner distance of ▫$W$▫ and union of all Steiner trees of ▫$W$▫ form a Steiner interval. Both of them are described for the lexicographic product in the present work. We also give a complete answer for the following invariants with respect to the Steiner convexity: the Steiner number, the rank, the hull number, and the Carathéodory number, and a partial answer for the Radon number. At the end we locate and repair a small mistake from [J. Cáceres, C. Hernando, M. Mora, I. M. Pelayo, M. L. Puertas, On the geodetic and the hull numbers in strong product graphs, Comput. Math. Appl. 60 (2010) 3020--3031]. teorija grafov leksikografski produkt Steinerjeva konveksnost Steinerjeva množica Steinerjeva razdalja graph theory lexicographic product Steiner convexity Steiner set Steiner distance true false false Angleški jezik Angleški jezik Delo ni kategorizirano 2015-07-10 15:31:16 2015-07-10 15:31:16 2022-05-31 03:09:02 2019-07-11 07:34:39 2012 0 0 str. 1-15 št. 1179 Vol. 50 2012 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 15706713 16322393 2232-2094 URN:SI:UM:DK:29O5SFB6 http://www.imfm.si/preprinti/PDF/01179.pdf 1 https://dk.um.si/Dokument.php?lang=slv&id=76566 Fakulteta za elektrotehniko, računalništvo in informatiko 0 0 0