The concept of inverse domination was introduced by Kulli V.R. and Sigarakanti S.C. [9] . Let D be a  -set of G. A dominating set D 1  V-D is called an inverse dominating set of G with respect to D. The inverse domination number   (G) is the order of a smallest inverse dominating set. Motivated by this definition we define another parameter as follows. Let D be a maximum independent set in G. An independent set S  V-D is called an inverse independent set with respect to D. The inverse

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... endence Number β 0 -1 (G) = max { S : S is an inverse independent set of G}.We find few bounds on inverse domination number and also initiate the study of the inverse independence number giving few bounds on inverse independence number of a graph.