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


B.K Ameenal
R Selvakumar

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.

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eISSN: 2141-2839
print ISSN: 2141-2820