20.500.12556/DKUM-92600 2-rainbow independent domination in complementary prisms A function f that assigns values from the set to each vertex of a graph G is called a 2-rainbow independent dominating function, if the vertices assigned the value 1 form an independent set, the vertices assigned the value 2 form another independent set, and every vertex to which 0 is assigned has at least one neighbor in each of the mentioned independent sets. The weight of this function is the total number of vertices assigned nonzero values. The 2-rainbow independent domination number of G, , is the minimum weight of such a function. Motivated by a real-life application, we study the 2-rainbow independent domination number of the complementary prism of a graph G, which is constructed by taking G and its complement , and then adding edges between corresponding vertices. We provide tight bounds for , and characterize graphs for which the lower bound, i.e. , is attained. The obtained results can, in practice, enable the prediction of the cost estimate for a given communication or surveillance network. graph theory domination 2-rainbow independent domination complementary prism teorija grafov dominacija true false true Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC) = Brazilian Society of Computational and Applied Mathematics (Springer) Angleški jezik Slovenski jezik https://link.springer.com/journal/40314 © The Author(s) 2025 Članek v reviji 2025-04-23 15:38:58 2025-04-23 15:38:58 2026-01-26 14:36:29 0000-00-00 00:00:00 2025 0 0 13 str. [article no.] 235 Vol. 44 Apr. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2024-08-30 2025-03-15 2025-04-11 519.17 233075971 10.1007/s40314-025-03189-9 1807-0302 s40314-025-03189-9.pdf s40314-025-03189-9.pdf 1 A2CAEA14B34529029F11313265737FA1 974e9fb8c20b5fb701f590265893effa1351850e5dc43f9be7ece00f681d558f 75e3f4cc-2048-11f0-adc7-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=190488 https://link.springer.com/article/10.1007/s40314-025-03189-9#additional-information 0 04a26f70-fabc-11f0-9b4e-00155d00018d https://dk.um.si/Dokument.php?lang=slv&id=202567 Fakulteta za elektrotehniko, računalništvo in informatiko 0 0 0