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A set  D  of vertices in a connected graph  G  is said to be an  independent 2-point set dominating set  (or in short i-2psd set) of  G  if  D  is an independent set and for every non-empty subsetthere exists a non-empty subsethaving at most 2 vertices such that the induced subgraphis connected. We call a graph to be an i-2psd graph if it possesses an i-2psd set. In this article, we explore i-2psd graphs. We first provide complete structural characterization of separable i-2psd graphs and thereafter, in our quest to characterize i-2psd blocks, we characterize hexagon-free bipartite i-2psd blocks and exhibit a family of non-bipartite i-2psd blocks.

Independent 2-point set domination in graphs - II