On k-rainbow independent domination in graphs

Tadeja Kraner Šumenjak, Douglas F. Rall and Aleksandra Tepeh

Applied Mathematics and Computation, 2018, vol. 333, issue C, 353-361

Abstract: In this paper, we define a new domination invariant on a graph G, which coincides with the ordinary independent domination number of the generalized prism G□Kk, called the k-rainbow independent domination number and denoted by γrik(G). Some bounds and exact values concerning this domination concept are determined. As a main result, we prove a Nordhaus–Gaddum-type theorem on the sum for 2-rainbow independent domination number, and show if G is a graph of order n ≥ 3, then 5≤γri2(G)+γri2(G¯)≤n+3, with both bounds being sharp.

Keywords: Domination; k-rainbow independent domination; Nordhaus–Gaddum (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:333:y:2018:i:c:p:353-361

DOI: 10.1016/j.amc.2018.03.113

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