A Note on Gourava Index for an Algebraic Structure Graphs

Abstract

Molecular descriptors such as topological indices are widely employed in the construction of quantitative structure-activity relationships (QSAR), quantitative structure-property relationships (QSPR), and quantitative structure-toxicity relationships (QSTR). Gourava index is one of the very important topological indexes that have been recently defined. In this study, the Gourava index will be obtained for the zero-divisor graph of monogenic semigroups.

Keywords

• Gourava index
• monogenic semigroup
• topological index

References

1. [1] Akg¨unes¸ N., C¸ a˘gan B., On the Dot Product of Graphs over Monogenic Semigroups, Applied Mathematics and Computation. Vol:322 (2018), 1-5.
2. [2] Akg¨unes¸, N., Nacaroglu, Y., On the sigma index of the corona products of monogenic semigroup graphs. Journal of Universal Mathematics. Vol:2, No.1 (2019), 68-74.
3. [3] Anderson D.F., Livingston P.S., The Zero-Divisor Graph of Commutative Ring, Journal of Algebra. Vol:217 (1999), 434-447.
4. [4] Anderson D.F., Badawi A., On the Zero-Divisor Graph of a Ring, Commun. Algebra. Vol:36, No.8 (2008), 3073-3092.
5. [5] Badawi A., On the Dot Product Graph of a Commutative Ring, Commun. Algebra. Vol:43 (2015), 43-50.
6. [6] Beck I., Coloring of Commutative Ring, Journal of Algebra. Vol:116 (1988), 208-226.
7. [7] Das K.C., Akg¨unes¸ N., C¸ evik A.S., On a Graph of Monogenic Semigroups, J. Inequal. Appl. Vol: 2013, No.44 (2013).
8. [8] DeMeyer F.R, DeMeyer L., Zero-Divisor Graphs of Semigroups, Journal of Algebra. Vol: 283 (2005), 90-198.

9. [9] DeMeyer F.R, McKenzie T., Schneider K., The Zero-Divisor Graph of a Commutative Semigroup, Semigr. Forum. Vol: 65 (2002), 206-214.
10. [10] DeMeyer L., Greve L., Sabbaghi A., Wang J., The Zero-Divisor Graph Asoociated to a Semigroup, Commun. Algebra. Vol:38, No.9 (2010), 3370-3391.
11. [11] Esen, B., Saralar Aras, I., C¸ okgenler Konusunun ¨O ˘gretiminde RETA Modelinin ¨Og˘rencilerin Bas¸arı ve Algılarına Etkisi, Necmettin Erbakan U¨ niversitesi Ere˘gli E˘gitim Fak¨ultesi Dergisi. Vol:4, No.2 (2022), 96-121.
12. [12] Furtula B., Gutman I., A forgotten topological index. J. Math. Chem. Vol:53, No.4 (2015), 1184–1190.
13. [13] Gutman I., Geometric approach to Degree-Based Topological Indices: Sombor Indices, MATCH Commun. Math. Comput. Chem. Vol:86 (2021), 11-16.
14. [14] Gutman I., Ruˇsˇci´c B., Trinajsti´c N., Wilcox C.F., Graph theory and molecular orbitals. XII. Acyclic polyenes. ´ J. Chem. Phys. Vol:62 (1975). P. 3399–3405.
15. [15] Gutman, I., Trinajsti´c, N., Graph theory and molecular orbitals. Total p-electron energy of alternant hydrocarbons. Chemical physics letters. Vol:17, No.4 (1972), 535-538.
16. [16] Hacibeyoglu, M., C¸ elik, M., Erdas¸ C¸ ic¸ek, O¨ ., En Yakın Koms¸u Algoritması ile Binalarda Enerji Verimlilig˘i Tahmini. Necmettin Erbakan U¨ niversitesi Fen Ve M¨uhendislik Bilimleri Dergisi, Vol:5, No.2 (2023), 28-37.
17. [17] Kulli, V. R., The Gourava indices and coindices of graphs. Annals of Pure and Applied Mathematics. Vol:14, No.1 (2017), 33-38.
18. [18] Kulli, V. R. The Gourava index of four operations on graphs. Mathematical Combinatorics, Vol:4 (2018), 65-67.
19. [19] Nacaroglu, Y., On Leap Zagreb Indices of A Special Graph Obtained by Semigroups. Journal of Universal Mathematics. Vol:6, No.3 (2023), 16-26.
20. [20] Nacaroglu, Y., On Join Operation of Graphs by Obtained Monogenic Semigroups. Turkish Journal of Mathematics and Computer Science. Vol:13, No.1 (2021), 57-62.
21. [21] Nacaroglu, Y., Maden, A.D., The multiplicative Zagreb coindices of graph operations. Utilitas Mathematica. Vol:102 (2017), 19-38.