Computing the Forgotten Topological Index for Zero Divisor Graphs of MV-Algebras

Year 2021, Volume: 11 Issue: 4, 3072 - 3085, 15.12.2021

Necla Kırcalı Gürsoy

https://doi.org/10.21597/jist.944846

Cited By: 1

Abstract

Topological indices are numerical values in graphs. Recently, they have been an attractive topic and multidisciplinary research area in mathematics, computer science, chemistry, pharmacy, and etc. In this work, we investigate the Forgotten index of zero divisor graphs of MValgebra. Firstly, using isomorphism between 𝐿𝑛 and 𝑛-element MV-chain, we generalize the Forgotten topological index for zero divisor graph of 𝐿𝑛 where 𝑛 > 5. Then, the Forgotten index of zero divisor graph for MV-algebras which have cardinality 5,6,7,8 is computed with supporting samples.

Keywords

Forgotten index, topological index, MV-algebra, zero divisor graph, graph theory

References

• Aijaz M, Pirzada S, 2020. Annihilating-ideal graphs of commutative rings, Asian-Eur. J. Math. 13(1), 1-12.
• Akbari S, Kiani D, Mohammadi F, Moradi S, 2009. The total graph and regular graph of a commutative ring, J. PureAppl. Algebra 213, 2224-2228.
• Anderson DF, Livingston PS, 1999. The zero-divisor graph of a commutative ring, J Algebra 217, 434-447.
• Anderson DF, Badawi A, 2008. Total graph of a commutative ring, J. Algebra 320, 2706-2719. Ansari MA, Haidar A, Koam AN, 2018. On a graph associated to up-algebras. Mathematical and Computational Applications 23(4), 61.
• Asir T, Rabikka V, 2021. The Wiener index of the zero-divisor graph of Zn, Discrete Appl. Math., 1-11.
• Beck I, 1988. Coloring of commutative rings, J Algebra 116(1), 208-226.
• Chang CC, 1958. Algebraic analysis of many valued logics. Transactions of the American Mathematical society, 88(2), 467-490.
• Chartrand G, Lesniak L, Zhang P, 2016. Graphs & digraphs, sixth edition. Textbooks in mathematics. CRC Press, Taylor & Francis Group, Boca Raton.
• Cignoli RL, d'Ottaviano IM, Mundici D, 2013. Algebraic foundations of many-valued reasoning (Vol. 7). Springer Science & Business Media.
• Das K, Cevik AS, Cangul IN, Shang Y, 2021. On Sombor Index, Symmetry 13(1), 1-12.
• Furtula B, Gutman I, 2015. A forgotten topological index. J. Math. Chem. 53 (4), 1184–1190.
• Gan A, Yang Y, 2020a. The zero-divisor graphs of mv-algebras. Soft Computing 24(8), 6059-6068.
• Gan A, Yang Y, 2020b. Annihilator graphs of mv-algebras. Journal of Algebra and its Applications p. 1-18.
• Ghanbari N, Alikhani S, 2021. Sombor index of certain graphs, arXiv preprint.
• Gutman I, 2021a. Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86, 11-16.
• Gutman I, 2021b. Some basic properties of Sombor indices, Open J. Discrete Appl. Math. 4(1), 1-3.
• Harary F, 1999. Graph Theory. Reading, MA: Perseus Books.
• Mundici D, 2007. MV-algebras. URL https://www.matematica.uns.edu.ar/IXCongresoMonteiro/ Comunicaciones/Mundici_tutorial.pdf
• Reti T, Doslic T, Ali A, 2021. On the Sombor index of graphs, Contrib. Math. 3, 11-18.
• Salehifar S, Khashyarmanesh K, Afkhami M, 2017. On the annihilator-ideal graph of commutative rings, Ricerche mat.66, 431-447.
• Shaveisi F, 2016. Some Results on Annihilating-ideal Graphs, Canad. Math. Bull. 59(3), 641-651.
• Singh P, Bhat VK, 2020. Adjacency matrix and Wiener index of zero divisor graph Γ (Zn), J. Appl. Math. Comput., 1-16.
• Sinha D, Rao AK, 2018. A note on co-maximal graphs of commutative, AKCE Int. J. Graphs Comb. 15(1), 112-114.
• Tehranian A, Maimani HR, 2011. A Study of the Total Graph, Iran. J. Math. Sci. Inform. 6(2), 75-80.
• Wang HJ, 2008. Graphs associated to co-maximal ideals of commutative rings, J. Algebra 320, 2917-2933.
• Ye M, Wu T, 2012. Co-maximal ideal graphs of commutative rings, J. Algebra Appl. 11(6), 1-14.
• Zhou T, Lin Z, Miao L, 2021. The Sombor index of trees and unicyclic graphs with given matching number, preprint.