Combined Product of Two RL-graphs and It’s Applications
محورهای موضوعی : Transactions on Fuzzy Sets and Systems
Mohammad Mehdi Zahedi
1
,
Elham Raisi Sarbizhan
2
1 - Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran.
2 - Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran.
کلید واژه: $RL$-graph, Regular $RL$-graph, Combined product of two $RL$-graphs,
چکیده مقاله :
This paper introduces the notion of the combined product of two RL-graphs while it is an RL-graph. It is stated that the combined product has commutative properties, i.e., G ⊠ H and H ⊠ G are two isomorphic RL-graphs. Moreover, it is shown under a theorem that two isomorphic RL-graphs G and G′ and two isomorphic RL-graphs H and H′ have isomorphic combined products G ⊠ H and G′ ⊠ H′. Further, it is investigated the relationships between these graphs and their operations by some notions such as strong RL-graph, regular RL- graph, and totally regular RL-graph. Afterward, it is displayed in a theorem that the combined product of two regular (α-regular, complete, connected) RL-graphs is a regular (α-regular, complete, connected) RL-graph. It is also shown in theorems what properties certain types of RL-graphs combined will have. Also, these notions and theorems are clarified by some examples. The combined product of two RL-graphs has many applications in various fields, such as probability sciences, urban planning, etc. In this article, only two of these applications, which determine the impact of effective factors on people’s quality of life and factors effective in raising the production of a factory, are stated and they are clarified by an example
This paper introduces the notion of the combined product of two RL-graphs while it is an RL-graph. It is stated that the combined product has commutative properties, i.e., G ⊠ H and H ⊠ G are two isomorphic RL-graphs. Moreover, it is shown under a theorem that two isomorphic RL-graphs G and G′ and two isomorphic RL-graphs H and H′ have isomorphic combined products G ⊠ H and G′ ⊠ H′. Further, it is investigated the relationships between these graphs and their operations by some notions such as strong RL-graph, regular RL- graph, and totally regular RL-graph. Afterward, it is displayed in a theorem that the combined product of two regular (α-regular, complete, connected) RL-graphs is a regular (α-regular, complete, connected) RL-graph. It is also shown in theorems what properties certain types of RL-graphs combined will have. Also, these notions and theorems are clarified by some examples. The combined product of two RL-graphs has many applications in various fields, such as probability sciences, urban planning, etc. In this article, only two of these applications, which determine the impact of effective factors on people’s quality of life and factors effective in raising the production of a factory, are stated and they are clarified by an example
1] A. Arenas, A. Diaz-Guilera, J. Kurths, Y. Moreno and C. Zhou, Synchronization in complex networks, Physics Reports, 469 (2008), 93-153.
[2] A. Barrat, M. Barthelemy and A. Vespignani, Dynamical processes in complex networks, Cambridge University Press, (2008).
[3] N. L. Biggs, E. K. Lioyd and R. J. Wilson, Graph theory 1736-1936, Oxford University Press, (1986).
[4] K. Blount and C. Tsinakis, The structure of residuated lattices. International Journal of Algebra and Computation, 13 (2003), 437-461.
[5] J. A. Bondy and U. S. R. Murty, Graph theory with applications, New York, Amsterdam, (1998).
[6] J. A. Bondy and U. S. R. Murty, Graph theory. Springer, London, (2008).
[7] A. Kauffman, Introduction a La theorie des sous-ensembles flous: A L’Usage Des Ingenieurs (Fuzzy Sets Theory), Tome III, Masson Et Cie, Editeurs, (1975).
[8] J. N. Mordeson and S. Mathew, Mathematics of Uncertainty for Coping with World Challenges: Climate Change, World Hunger, Modern Slavery, Coronavirus, Human Trafficking, Springer International Publishing, (2021).
[9] E. Raisi Sarbizhan, M. M. Zahedi and M. Shamsizade, L-graph automata and some applications, The Computer Journal, 23, (2022).
[10] E. Raisi Sarbizhan and M. M. Zahedi, Maximal product of two L-graph automata and some applications, Iranian Journal of Fuzzy Systems, 19(3) (2022), 107-126.
[11] E. Raisi Sarbizhan and M. M. Zahedi, On kronecker product of two RL-graphs and related results, J. Mahani Math. Res. Cent., 11(3), (2022), 87-107.
[12] E. Raisi Sarbizhan and M. M. Zahedi, The behavior of L-graph automata, Proceedings of 2022 9th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), Iran, (2022), 430-435.
[13] E. Raisi Sarbizhan and M. M. Zahedi, Some Properties of Maximal Product of Two RL-graphs, Proceedings of 2022 The First Seminar on Algebraic Logic, (2022), 1-6.
[14] A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications, 35, (1971), 512-517.
[15] L. A. Zadeh, Fuzzy sets, Information and Control, 8, (1965) 338-335.
[16] M. M. Zahedi, and E. Raisi Sarbizhan, Some properties of L-graphs, Proceedings of 2022 9th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), Iran, (2022), 1-5.
[17] M. Ward and R. P. Dilworth, Residuated lattices. Transactions of The American Society, 45, (1939), 335-354.
[18] D. B. West, Introduction to graph theory, 2, Pearson Education, India, (2001).
