Fenilenlerin Birinci ve İkinci Zagreb İndeksleri için Yeni Formüller ve Yeni Sınırlar

Yıl 2024, , 468 - 475, 18.06.2024

Elif Eryaşar , Esra Öztürk Sözen , Şerife Büyükköse

https://doi.org/10.31466/kfbd.1362864

Cited By: 1

Öz

Graf teorisi, kimyasal yapıları temsil etmek ve analiz etmek için yaygın olarak kullanılır. Ayrıca graflar için geliştirilen topolojik indeksler fizikokimyasal ve biyoaktivite gibi kimyasal yapıların ilişkileriyle de bağlantılıdır. Topolojik indeksler QSPR-QSAR analizinde yaygın olarak kullanılmaktadır ve kimyasal graf teorisinde birçok uygulama bulmuştur. Bilinen en eski dereceye bağlı topolojik indeksler birinci ve ikinci Zagreb indeksleridir. Bu indeksler kimyasal yapılarda geniş uygulama alanı bulmuştur. Aromatik ve antiaromatik halkalar içeren fenilenler benzersiz fizikokimyasal özellikler sergilemektedir ve fenilenler için çok çeşitli çalışmalar bulunmaktadır. Bu yazıda fenilenlerin birinci ve ikinci Zagreb indekslerinin moleküler yapıları için bazı yeni formüller ve alt sınırlar sunuyoruz. Ayrıca graf algoritmalarından BFS algoritması yöntemi ilk kez kimyasal yapıların sınır çalışmasında kullanılmıştır.

Anahtar Kelimeler

Birinci ve ikinci Zagreb indeksleri, BFS Algoritması, fenilenler

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

First and second Zagreb indices, BFS algorithms, phenylenes

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.
• Jacob, K., Clement, J., Arockiaraj, M., Paul, D., and Balasubramanian K. (2023). Topological characterization and entropy measures of tetragonal zeolite merlinoites. Journal of Molecular Structure, 1277, 134786.
• Marković, S., and Gutman, I. (1999). Spectral moments of the edge adjacency matrix in molecular graphs. Benzenoid hydrocarbons. Journal of Chemical Information and Computer Sciences, 39(2), 289-293.
• Marković, S., Marković, Z., and McCrindle, R. I. (2001). Spectral moments of phenylenes. Journal of Chemical Information and Computer Sciences, 41(1), 112-119.
• Rashid, M. A., Ahmad, S., Siddiqui, M. K., Jahanbani, A., Sheikholeslami, S. M., and Shao, Z. (2022). New bounds for the Estrada index of phenylenes. Polycyclic Aromatic Compounds, 42, 1061-1077.
• Scheffler, R. (2022). On the recognition of search trees generated by BFS and DFS. Theoretical Computer Science, 936, 116-128.
• Toda, F., and Garratt, P. (1992). Four-membered ring compounds containing bis (methylene) cyclobutene or tetrakis (methylene) cyclobutane moieties. Benzocyclobutadiene, benzodicyclobutadiene, biphenylene, and related compounds. Chemical Reviews, 92(8), 1685-1707.
• Vollhardt, K. P. C., and Mohler, D. L. (1996). The Phenylenes: syntheses, properties, and reactivity. ChemInform, 27(40).
• Wiener, H. (1947) Structural determination of paraffin boiling points. Journal of the American Chemical, 69(1), 17–20.
• Wu, T. (2016). Two classes of topological indices of phenylene molecule graphs. Mathematical Problems in Engineering.
• Yang, Y., and Wang, D. (2019). Extremal phenylene chains with respect to the Kirchhoff Index and degree-based topological indices. International Journal of Applied Mathematics, 49(3).
• Yoo, A., Chow, E., Henderson, K., McLendon, W., Hendrickson, B., and Çatalyürek U. (2005). A scalable distributed parallel breadth-first search algorithm on BlueGene/L, SC’05. Proceedings of the 2005 ACM/IEEE Conference on Supercomputing, 25.
• Yousefi-Azari, H., Yazdani, J., Bahrami, A., and Ashrafi, A. R. (2007). Computing PI and Szeged indices of multiple phenylenes and cyclic hexagonal-square chain consisting of mutually isomorphic hexagonal chains. Journal of the Serbian Chemical Society, 72(11), 1063-1067.