Characterization of rough identity-summand graph

This research aims to construct multiple Gray code generations from the structural features of a rough identity-summand graph. To establish the nature of the rough identity-summand graph defined for the filters of a rough bi-Heyting algebra, the generation of distinct complete bipartite graphs from [Formula: see text] is presented in detail. Then it is demonstrated that the union of these unique complete bipartite graphs forms the subgraph of [Formula: see text]. Each complete bipartite graph is considered in determining various lengths in the generation of Gray codes. The added advantage is two Gray codes for each of the complete bipartite graphs induced by the lower and upper approximations of [Formula: see text].