On Some Graphs Based on the Ideals of JU-Algebras
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Abstract
We will construct few types of simple graphs (with no multiple edges or loops) based on the ideal annihilator, right ideal annihilator, left ideal annihilator for JU-algebras. We will also study some graph invariants, such as connectivity, regularity, and planarity for these graphs.
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References
- I. Beck, Coloring of Commutative Rings, J. Algebra. 116 (1988), 208–226. https://doi.org/10.1016/0021-8693(88)90202-5.
- R. Diestel, Graph Theory, Springer, New York, 1997.
- R. Halas, M. Jukl, On Beck’s Coloring of Posets, Discr. Math. 309 (2009), 4584–4589. https://doi.org/10.1016/j.disc.2009.02.024.
- Y. Imai, K. Iseki, On Axiom Systems of Propositional Calculi, XIV, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 19–22. https://doi.org/10.3792/pja/1195522169.
- K. Iseki, An Algebra Related With a Propositional Calculus, Proc. Japan Acad. Ser. A Math. Sci. 42 (1966), 26–29. https://doi.org/10.3792/pja/1195522171.
- Y.B. Jun, K.J. Lee, Graphs Based on BCK/BCI-Algebras, Int. J. Math. Math. Sci. 2011 (2011), 616981. https://doi.org/10.1155/2011/616981.
- A. Mohammadian, A. Erfanian, M. Farrokhi, Planar, Toroidal and Projective Generalized Peterson Graphs, In: Proceeding of the 7th Algebraic Combinatorics Conference of Iran, October 16-17, 2014, Ferdowsi University of Mashhad, Mashhad, Iran, 2014.
- F. Shahsavar, M. Afkhami, K. Khashyarmanesh, On End-Regular, Planar and Outer Planar of Zero-Divisor Graphs of Posets, In: Proceeding of the 6th Algebraic Conference, Iran, 30-31 October 2013, University of Mazandaran, Babolsar, Iran, 2013.
- A.T. Meikola, Graphs of BCI/BCK-Algebras, Turk. J. Math. 42 (2018), 1272-1293.
- A.T. Meikola, Twelve Kinds of Graphs of Lattice Implication Algebras Based on Filter and LI-Ideal, Cankaya Univ. J. Sci. Eng. 17 (2020), 11–40.
- C. Prabpayak, U. Leerawat, On Ideals and Congruences in KU-Algebras, Sci. Magna. 5 (2009), 54–57.
- C. Prabpayak, U. Leerawat, On Isomorphisms of KU-Algebras, Sci. Magna. 5 (2009), 25–31.
- N. Yaqoob, S.M. Mostafa, M.A. Ansari, On Cubic KU-Ideals of KU-Algebras, ISRN Algebra. 2013 (2013), 935905. https://doi.org/10.1155/2013/935905.
- S.M. Mostafa, M.A. Abd-Elnaby, M.M.M. Yousef, Fuzzy Ideals of KU-Algebras, Int. Math. Forum. 6 (2011), 3139– 3149.
- S.M. Mostafa, M.A. Abd-Elnaby, O.R. Elgendy, Interval Valued Fuzzy KU-Ideals in KU-Algebras, Int. Math. Forum. 6 (2011), 3151–3159.
- M.A. Ansari, Rough Set Theory Applied to JU-Algebras, Int. J. Math. Comput. Sci. 16 (2021), 1371-1384.
- M.A. Ansari, A. Haider, A.N. Koam, On JU-Algebras and p-Closure Ideals, Int. J. Math. Comput. Sci. 15 (2020), 135–154.
- M.A. Ansari, A.N.A. Koam, Rough Approximations in KU-Algebras, Italian J. Pure Appl. Math. 40 (2018), 679–691.
- A.N.A. Koam, A. Haider, M.A. Ansari, Pseudo-Metric on KU-Algebras, Korean J. Math. 27 (2019), 131–140. https://doi.org/10.11568/KJM.2019.27.1.131.
- U. Ali, M.A. Ansari, M.U. Rehman, Pseudo-Valuations and Pseudo-Metric on JU-Algebras, Open J. Math. Sci. 3 (2019), 440–446. https://doi.org/10.30538/oms2019.0086.