On k-rainbow independent domination in graphs

摘要

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.