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Given a simple graph on n vertices, currently 1.7159n is the best upper bound on the number of minimal dominating sets.  This bound has been improved for some classes of graphs.  In this article, the bound 1.7159n is improved for the class of simple loop-free connected graphs having pendant vertices, leading up to the corresponding results for simple loop-free connected hypergraphs

IMPROVED UPPER BOUND ON THE NUMBER OF MINIMAL DOMINATING SETS IN PENDANT GRAPHS