The inverse strong non-split r-domination number of a graph

Abstract

In this paper, we define the notions of inverse strong non-split r-dominating set and inverse strong non-split r-domination number γ′snsr(G) of a graph G. We characterize graphs for which γsnsr(G) + γ′snsr(G) = n, where γsnsr(G) is the strong non-split r-domination number of G. We get many bounds on γ′snsr(G). Nordhaus-Gaddum type results are also obtained for this new parameter

Keywords: r-independent set, r-dominating set, strong non-split r-dominating set, inverse strong non-split r-dominating set, strong non-split r-domination number and inverse strong non-split r-domination number.