20.500.12556/RUP-2624 A note on domination and independence-domination numbers of graphs Vizing's conjecture is true for graphs ▫$G$▫ satisfying ▫$\gamma^i(G) = \gamma(G)$▫, where ▫$\gamma(G)$▫ is the domination number of a graph ▫$G$▫ and ▫$\gamma^i(G)$▫ is the independence-domination number of ▫$G$▫, that is, the maximum, over all independent sets ▫$I$▫ in ▫$G$▫, of the minimum number of vertices needed to dominate ▫$I$▫. The equality ▫$\gamma^i(G) = \gamma(G)$▫ is known to hold for all chordal graphs and for chordless cycles of length ▫$0 \pmod{3}$▫. We prove some results related to graphs for which the above equality holds. More specifically, we show that the problems of determining whether ▫$\gamma^i(G) = \gamma(G) = 2$▫ and of verifying whether ▫$\gamma^i(G) \ge 2$▫ are NP-complete, even if ▫$G$▫ is weakly chordal. We also initiate the study of the equality ▫$\gamma^i = \gamma$▫ in the context of hereditary graph classes and exhibit two infinite families of graphs for which ▫$\gamma^i < \gamma$▫. Vizing's conjecture domination number independence-domination number weakly chordal graph NP-completeness hereditary graph class IDD-perfect graph true true false Angleški jezik Angleški jezik Neznano 2013-10-15 12:07:27 2013-10-15 12:07:27 2024-03-01 12:08:29 0000-00-00 00:00:00 2013 0 0 str. 89-97 no. 1 Vol. 6 2013 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 1855-3966 16465753 1024423764 RAZ_Milanic_Martin_i2013.pdf RAZ_Milanic_Martin_i2013.pdf 1 653E076C3F1DE2F04B4C14DB3DD5D0BA 81ede94dadb060dc9134231fbfa1b27409bbd87121c2398f3294a7479b659217 76c8bb1a-c3d6-11ed-b5df-005056bf369b https://repozitorij.upr.si/Dokument.php?lang=slv&id=25907 Založba Univerze na Primorskem 0 0 0