20.500.12556/DKUM-93806 On the b-chromatic number of rooted product graphs The b-chromatic number of a graph G was defined by Irving and Manlove in 1999 as the largest integer k for which G admits a proper coloring with k colors such that every color class (in this proper coloring) has a vertex that is adjacent to at least one vertex in every other color class. The b-chromatic number has been studied in many contexts, including for various graph products. The rooted product, defined by Godsil and McKay in 1978, is not yet among these. We find bounds for the b-chromatic number of the rooted product of two graphs in terms of the b-chromatic numbers and degrees of the factors, along with some new parameters that we define. Moreover, we give sufficient conditions for equality to hold in these bounds. We refine our results, sometimes to exact values, when one or both of the factors is a path, cycle, complete graph, star, or wheel. graph theory chromatic number b-chromatic number teorija grafov kromatično število b-kromatično število true false true Angleški jezik Slovenski jezik Znanstveno delo 2025-07-22 14:06:40 2025-07-22 14:06:40 2025-07-23 03:11:07 0000-00-00 00:00:00 2025 0 0 str. 3805-3815 št. 11 Letn. 39 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2024-12-01 2025-01-26 0000-00-00 519.17 232792067 10.2298/FIL2511805B 0354-5180 RAZ_Bockting-Conrad_Sarah_2025.pdf RAZ_Bockting-Conrad_Sarah_2025.pdf 1 996D87F1883EEA0907A8817A4D3C4D35 8ca9b9fc98c48b1d8fd41c093dee8aa0c8babf08841eca0447cf5046dbaeedf4 546ffff8-66f4-11f0-b4a7-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=193943 https://www.pmf.ni.ac.rs/filomat-content/2025/39-11/39-11-22-26330.pdf 0 b78b66a0-66f4-11f0-b4a7-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=193944 Fakulteta za naravoslovje in matematiko 0 0 0