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

Yıl 2024, Cilt: 14 Sayı: 2, 468 - 475, 18.06.2024

Elif Eryaşar Esra Öztürk Sözen Şerife Büyükköse

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

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

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