New Formulas and New Bounds for the First and Second Zagreb Indices of Phenylenes
Öz
Graph theory is widely used to represent and analyze chemical structures. In addition, topological indices developed for graphs have a connection with the relationships of chemical structures such as physicochemical and bioactivity. Topological indices are widely used in QSPR-QSAR analysis and have found many applications in chemical graph theory. The oldest known degree-dependent topological indices are the first and second Zagreb indices. These indices have found wide application in chemical structures. Phenylenes containing aromatic and antiaromatic rings exhibit unique physicochemical properties and there is a wide variety of studies on phenylenes. In this article, we present some new formulas and lower bounds for the first and second Zagreb indices molecular structures of phenylenes. In addition, the BFS algorithm method, which is one of the graph algorithms, was used for the first time for the boundary study of chemical structures.
Anahtar Kelimeler
Kaynakça
- Çölkesen, R. (2015). Bilişim Matematiği (First Edition). İstanbul: Papatya Publishing, 349-382.
- Das, K. C., and Mondal, S. (2023). On neighborhood inverse sum indeg index of molecular graphs with chemical significance. Information Sciences, 623, 112-131.
- Deng, H., Chen, S., and Zhang J. (2007). The PI index of phenylenes. Journal of Mathematical Chemistry, 41, 63-69.
- Eryaşar, E., and Büyükköse, Ş. (2023). Lower Bounds for Zagreb Indices of RNA Graphs Using Graph Algorithms. Journal of Mathematics and Statistical Science, 9, 1-9.
- Faust, R., Glendening, E. D., Streitwieser, A., Vollhardt, K. P. C., Weinhold, F. (1992). Ab initio study of. sigma.-and. pi. effects in benzenes fuse to four-membered rings: rehybridization, delocalization, and antiaromaticity, Journal of the American Chemical Society, 114(21), 8263-8268 .
- Feng, Q., and Hu, Z. (2011). On the Zagreb index of random recursive trees. Journal of Applied Probability, 48(4), 1189-1196.
- Havare, Ö. Ç., and Havare, A. K. (2022). Computation of the forgotten topological index and co-index for carbon base nanomaterial. Polycyclic Aromatic Compounds, 42(6), 3488-3500.
- Havare, Ö.Ç. (2024). Reformulated zagreb indices of some cycle-related graphs and linear [n]-phenylenes. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 7(1), 33-45.
- Gutman, I., and Trinajsti´c, N. (2005). Graph theory and molecular orbitals. Berlin: New Concepts II, Springer.
- Hopcroft, J., and Tarjan, R. (1973). Algorithm 447: Efficient algorithms for graph manipulation. Communications of the ACM, 16(6), 372-378.
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