THE INVERSE DISTANCE – 2 DOMINATION IN GRAPHS AND ITS APPLICATIONS

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A. Lakshmi
K. Ameenal Bibi

Abstract

Let G = (V, E) be a simple, finite, connected and undirected graph. Let D⊆G be the non-empty subset of G such that D is the minimum distance - 2 dominating set in the graph G = (V, E). If V-D contains a distance - 2 dominating set Dʹ of G, then Dʹ is called an inverse distance - 2 dominating set with respect to D. The inverse distance - 2 domination number γ≤ 2-1 (G) of G is the cardinality of a minimum inverse distance - 2 dominating set of G. In this paper, we defined the notion of an inverse distance - 2 domination number of graphs. We get many bounds on inverse distance - 2 domination number. Exact values of this new parameter are obtained for some standard graphs and also its relationship with other domination parameters was obtained. Nordhaus - Gaddum type results are also obtained for this new parameter.

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