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Letbe a finitely generated free semimodule over a semiringwith identity having the invariant basis number property. Letbe a basis ofand letThen the skeleton of  a  with respect tois defined asThe reduced non-zero component union graphofwith respect tois the simple undirected graph with vertex setwhere at least one of the  c i’s is zeroand two distinct verticesare adjacent if and only ifIn this paper, we show that the graphis connected and find its domination number, clique number and chromatic number. In the case of finite semirings, we determine the order, size and degrees of vertices inAlso, we give the characterization for planarity of

Reduced non-zero component union graph of free semi-modules