20.500.12556/RUP-21996 The domination and independent domination numbers of some families of snarks Dominacijsko in neodvisno dominacijsko število nekaterih družin snarkov A dominating set of a graph G is a set S ⊆ V (G) such that every vertex in V (G) either belongs to S or is adjacent to some vertex in S. The domination number is the minimum cardinality of a dominating set of G. An independent dominating set of G is a dominating set that is also independent. The minimum cardinality of an independent dominating set of G is the independent domination number of G. Given the computational complexity of these problems, extensive research has been done on finding bounds or determining these parameters for classes of graphs, especially cubic graphs. Furthermore, determining how far apart these parameters are is also a challenging problem. In this work, we establish some bounds for the domination number and the independent domination number for families of cubic graphs, in particular for Generalized Blanuša Snarks and for two families of Loupekine Snarks known as LP_0-snarks and LP_1-snarks. We also show that the parameters are equal for these graphs and conjecture that this equality holds for every snark. domination independent domination Generalized Blanuša Snarks Loupekine Snarks dominacija neodvisna dominacija posplošeni Blanuševi snarki Loupekineovi snarki true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-10-21 22:59:49 2025-10-21 22:59:49 2025-11-12 03:05:31 0000-00-00 00:00:00 2025 0 0 15 str. no. 3, [article no.] P3.01 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-04-29 51 1855-3974 https://doi.org/10.26493/1855-3974.3285.dc4 AMC_Pereira,Campos_2025.pdf AMC_Pereira,Campos_2025.pdf 1 A93AD7DA5203FDEB1D6D5E320C0B8D70 21df113f8c83566aafed6a09f7aacb0ccbd19739a128adae48ce7259ef975bbe 742d3502-aec1-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31931 Založba Univerze na Primorskem 0 0 0