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Inverse vertex covering number of a graph

Abstract Let G = (V, E) be a graph. Let D be a minimum vertex covering of G. If V – D contains a vertex cover D’ of G, then D’ is called an inverse vertex cover with respect to D. The inverse vertex covering number of G is the minimum cardinality of an inverse vertex cover of G. In this paper, we initiate a study of this new parameter and establish some results on this parameter.