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Paper details
Number 2 - June 2025
Volume 35 - 2025
Generation of Gray codes through the rough identity-summand graph of filters of a rough bi-Heyting algebra
Bashyam Praba, Lourdusamy Packiammal Anto Freeda
Abstract
This paper introduces the concept of filters in a rough bi-Heyting algebra. The rough bi-Heyting algebra defined through
the rough semiring offers interesting properties. Filters on this rough bi-Heyting algebra are to be described in terms
of the R-upset. Then a one-to-one correspondence between the filters, the principle ideal and R-upsets is established.
Various filters are characterized on this rough bi-Heyting algebra. For each filter, a rough identity-summand graph is
constructed. This rough identity-summand graph is proved to be a complete bipartite graph in certain cases involving pairs
of elements. When more than two elements are involved, a rough identity-summand graph exists and generates multiple
complete bipartite graphs. The number of distinct complete bipartite graphs generated from this graph is defined to be an
RBP number. The union of these distinct complete bipartite graphs forms a subgraph of the rough identity-summand graph.
Additionally, this study demonstrates how two transition sequences obtained from the distinct complete bipartite graphs of
the rough identity-summand graph can be utilized to generate Gray codes, making a substantial contribution.
Keywords
Heyting algebra, filter, identity-summand graph, complete bipartite graph, Gray code