Applied Mathematics and Scientific Computing pp 453-459 | Cite as

# An Algorithm for the Inverse Distance-2 Dominating Set of a Graph

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## Abstract

Let *G* = (*V*, *E*) be a simple, finite, connected, and undirected graph. Let *D* ⊆ *V* (*G*) be the non-empty subset of *V* (*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 *D*^{′} of *G*, then *D*^{′} is called an inverse distance-2 dominating set with respect to *D*. The inverse distance-2 domination number \({{\gamma }_{\leq 2}}^{-1}\left (G\right )\) of *G* is the minimum cardinality of the minimal inverse distance-2 dominating set of *G*. In this paper, we presented an algorithm for finding an inverse distance-2 dominating set of a graph.

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