A graph G=(V,E) with p vertices and q edges is said to be strongly equal odd even multiplicative if the vertices of G can be labeled with distinct integers from {1,2,3,…,p} such that labels induced on the edges by the product of the labels of end vertices are all distinct and Of^* (uv)=Ef^* (uv),where Of^* (uv)=number of edges with odd labeling under f^* and Ef^* (uv)= number of edges with even labeling under f^*. We discuss strongly equal odd even multiplicative labeling of star graph, double star graph bistar graph and lilly graph.