Sum Connectivity Index Under the Cartesian and Strong Products Graph of Monogenic Semigroup

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DOI: https://doi.org/10.28924/2291-8639-21-2023-94
Published: Aug 29, 2023
Cite as:
R. Rajadurai, G. Sheeja, Sum Connectivity Index Under the Cartesian and Strong Products Graph of Monogenic Semigroup, Int. J. Anal. Appl., 21 (2023), 94.

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R. Rajadurai, G. Sheeja

Abstract

This field’s main feature is to implement the sum connectivity index method. This sum connectivity index method can solve the monogenic semigroups under the cartesian and strong products. We will define for an undirected graph as SCI(GMS)=Σuv∈E(GMS) [dGMS(u)+dGMS(v)]−1/2, where dGMS(u) and dGMS(v) are degree of u and v in GMS respectively. Further, we investigate two different algorithms concerning topological index for computing cartesian and strong products of a monogenic semigroup with a detailed example.

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References

  1. B. Zhou, N. Trinajstić, On General Sum-Connectivity Index, J. Math. Chem. 47 (2009), 210-218. https://doi.org/10.1007/s10910-009-9542-4.
  2. Z. Du, B. Zhou, N. Trinajstić, On the General Sum-Connectivity Index of Trees, Appl. Math. Lett. 24 (2011), 402-405. https://doi.org/10.1016/j.aml.2010.10.038.
  3. S. Wang, B. Zhou, N. Trinajstić, On the Sum-Connectivity Index, Filomat, 25 (2011), 29-42. https://www.jstor.org/stable/24895554.
  4. X. Chen, General Sum-Connectivity Index of a Graph and Its Line Graph, Appl. Math. Comput. 443 (2023), 127779. https://doi.org/10.1016/j.amc.2022.127779.
  5. B. Aydin, N. Akgunes, I.N. Cangul, On the Wiener Index of the Dot Product Graph over Monogenic Semigroups, Eur. J. Pure Appl. Math. 13 (2020), 1231-1240. https://doi.org/10.29020/nybg.ejpam.v13i5.3745.
  6. S. Oğuz Ünal, Sombor Index over the Tensor and Cartesian Products of Monogenic Semigroup Graphs, Symmetry. 14 (2022), 1071. https://doi.org/10.3390/sym14051071.
  7. N. Akgüneş, Some Graph Parameters on the Strong Product of Monogenic Semigroup Graphs, Bal. Üniv. Biliml. Enst. Derg. 20 (2018), 412-420. https://doi.org/10.25092/baunfbed.418449.
  8. Z. Du, B. Zhou, N. Trinajstić, On the General Sum-Connectivity Index of Trees, Appl. Math. Lett. 24 (2011), 402-405. https://doi.org/10.1016/j.aml.2010.10.038.
  9. R. Xing, B. Zhou, N. Trinajstić, Sum-Connectivity Index of Molecular Trees, J. Math. Chem. 48 (2010), 583-591. https://doi.org/10.1007/s10910-010-9693-3.
  10. Z. Du, B. Zhou, N. Trinajstić, Minimum Sum-Connectivity Indices of Trees and Unicyclic Graphs of a Given Matching Number, J. Math. Chem. 47 (2009), 842-855. https://doi.org/10.1007/s10910-009-9604-7.
  11. Z. Du, B. Zhou, N. Trinajstić, Minimum General Sum-Connectivity Index of Unicyclic Graphs, J. Math. Chem. 48 (2010), 697-703. https://doi.org/10.1007/s10910-010-9702-6.
  12. Z. Du, B. Zhou, On Sum-Connectivity Index of Bicyclic Graphs, Preprint, (2009). http://arxiv.org/abs/0909.4577.
  13. K.C. Das, N. Akgüneş, A.S. Çevik, On a Graph of Monogenic Semigroups, J. Inequal. Appl. 2013 (2013), 44. https://doi.org/10.1186/1029-242x-2013-44.
  14. N. Akgüneş, A.S. Çevik, A New Bound of Radius With Irregularity Index, Appl. Math. Comput. 219 (2013), 5750- 5753. https://doi.org/10.1016/j.amc.2012.11.081.
  15. L. Zhong, The Harmonic Index for Graphs, Appl. Math. Lett. 25 (2012), 561-566. https://doi.org/10.1016/j.aml.2011.09.059.
  16. B. Zhou, N. Trinajstić, On a Novel Connectivity Index, J. Math. Chem. 46 (2009), 1252-1270. https://doi.org/10.1007/s10910-008-9515-z.
  17. B. Lučić, N. Trinajstić, B. Zhou, Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons, Chem. Phys. Lett. 475 (2009), 146-148. https://doi.org/10.1016/j.cplett.2009.05.022.