Rough Identity-Summand Graph and Its Applications

This work aims to obtain various Gray code constructions from the structural properties 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 enumeration of distinct complete bipartite graphs from \(G(F_{X}(T))\) will be presented in detail. Then, it will be proved that the union of these distinct complete bipartite graphs forms the subgraph of \(G(F_{X}(T))\). This subgraph will be considered in identifying the various lengths of the Gray codes through two approximation transition sequences.