Generation of Gray codes through the rough identity-summand graph of filters of a rough bi-Heyting algebra

• Autorzy: Praba Bashyam , Anto Freeda Lourdusamy Packiammal

Identyfikatory

DOI

10.61822/amcs-2025-0026

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Heyting algebra; identity summand graph; complete bipartite graph; Gray code

PL

algebra Heytinga; graf dwudzielny; kod Graya

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2025
• Tom: Vol. 35, no. 2
• Strony: 371--385
• Opis fizyczny: Bibliogr. 24 poz., rys.

Twórcy

autor

Praba Bashyam

• Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Rajiv Gandhi Salai (OMR), Kalavakkam - 603 110 Chennai, Tamil nadu, India

autor

Anto Freeda Lourdusamy Packiammal

• Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Rajiv Gandhi Salai (OMR), Kalavakkam - 603 110 Chennai, Tamil nadu, India

Bibliografia

• [1] Atani, S.E., Hesari, S.D.P. and Khoramdel, M. (2014). The identity-summand graph of commutative semirings, Journal of the Korean Mathematical Society 51(1): 189-202.
• [2] Atani, S.E., Hesari, S.D.P. and Khoramdel, M. (2015a). Total identity-summand graph of a commutative semiring with respect to a co-ideal, Journal of the Korean Mathematical Society 52(1): 159-176.
• [3] Atani, S.E., Hesari, S.D.P., Khoramdel, M. and Sedghi, M. (2018). A semiprime filter-based identity-summand graph of a lattice, Le Matematiche 73(2): 297-318.
• [4] Atani, S.E., Hesari, S. and Khoramdel, M. (2015b). A co-ideal based identity-summand graph of a commutative semiring, Commentationes Mathematicae Universitatis Carolinae 56(3): 269-285.
• [5] Bondy, J.A. and Murthy, U.S.R. (1976). Graph Theory with Applications, London.
• [6] Chandrasekaran, V., Manimaran, A. and Praba, B. (2017). Ideals of a commutative rough semiring, Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science 10(59)(1): 67-82.
• [7] Ebrahimi Atani, S., Khoramdel, M., Dolati Pish Hesari, S. and Nikmard Rostamalipour, M. (2023). A graph associated to filters of a lattice, Journal of Algebraic Systems 10(2): 345-359.
• [8] Gallardo, C., Pelaitay, G. and Gallardo, C.S. (2023). T-rough symmetric heyting algebras with tense operators, Fuzzy Sets and Systems 466(16): 108455.
• [9] Halmos, P. and Givant, S. (2009). Introduction to Boolean Algebras, Springer, New York.
• [10] Liu, J.-B., Bao, Y., Zheng, W.-T. and Hayat, S. (2021). Network coherence analysis on a family of nested weighted n-polygon networks, Fractals 29(08): 2150260.
• [11] Liu, J.-B. and Pan, X.-F. (2016). Minimizing Kirchhoff index among graphs with a given vertex bipartiteness, Applied Mathematics and Computation 291(20): 84-88.
• [12] Liu, J.-B., Wang, X. and Cao, J. (2024). The coherence and properties analysis of balanced 2p-ary tree networks, IEEE Transactions on Network Science and Engineering.
• [13] Manimaran, A., Praba, B. and Chandrasekaran, V. (2017). Characterization of rough semiring, Afrika Matematika 28(5): 945-956.
• [14] Pawlak, Z. (1982). Rough sets, International Journal of Computer & Information Sciences 11(5): 341-356.
• [15] Praba, B., Chandrasekaran, V. and Manimaran, A. (2015). Semiring on rough sets, Indian Journal of Science and Technology 8(3): 280-286.
• [16] Praba, B. and Freeda, A. (2022). Rough bi-Heyting algebra and its applications in Heyting-Brouwer logic, submitted.
• [17] Praba, B., Manimaran, A., Deepa, G. and Muchtadi-Alamsyah, I. (2025). A note on principal rough ideals of a rough monoid, Advances in Mathematics: Scientific Journal 9(9): 6855-6861.
• [18] Praba, B. and Mohan, R. (2013). Rough lattice, International Journal of Fuzzy Mathematics and System 3(2): 135-151.
• [19] SanJuan, E. (2008). Heyting algebras with Boolean operators for rough sets and information retrieval applications, Discrete Applied Mathematics 156(6): 967-983.
• [20] Suparta, I.N. (2017). Some classes of bipartite graphs induced by gray codes, Electronic Journal of Graph Theory and Applications 5(2): 312-324.
• [21] Suparta, I.N. and Van Zanten, A. (2008). A construction of gray codes inducing complete graphs, Discrete Mathematics 308(18): 4124-4132.
• [22] West, D.B. (2001). Introduction to Graph Theory, Vol. 2, Prentice Hall Upper Saddle River.
• [23] Wilmer, E.L. and Ernst, M.D. (2002). Graphs induced by Gray codes, Discrete Mathematics 257(2-3): 585-598.
• [24] Yao, Y. (1998). Constructive and algebraic methods of the theory of rough sets, Information Sciences 109(1-4): 21-47.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).