Computation of Gutman index of Some Transformation Graphs

Year 2024, , 865 - 878, 01.06.2024

Merve Çakal Gökşen Bacak Turan

https://doi.org/10.21597/jist.1366169

Abstract

Graph theory is widely used today in many fields, including mathematical chemistry. In this area, numerous topological indices have been studied. Topological indices are used to define the topology of a molecular graph and relate it to various relevant properties. The most commonly used topological indices are degree-based and distance-based indices. This article examines the Gutman index, which holds great significance in chemistry. The Gutman index is a well-known topological index that simultaneously uses both degree and distance. These graphs are important because they enable the study of the properties of a graph under different transformations. It has been extensively studied in the literature and finds numerous applications in chemistry, physics, and other fields. Transformation graphs are graphs that are used to model molecular structures, physical networks, and algorithms in fields such as chemistry, computer science and physics. Original graph's symmetry, connectivity and other structural features can be revealed through these transformations. This article focuses on studying the Gutman index of some transformation graphs to provide a new topological index that can be used to examine their properties, and general formulas have been obtained.

Keywords

Graph theory, Transformation Graphs, Topological index, Gutman index

Bazı Transformasyon Çizgelerin Gutman İndeksinin Hesaplanması

Abstract

Çizge teorisi günümüzde birçok alanda kullanılmaktadır. Bu alanlardan biri de matematiksel kimyadır. Bu alanda birçok topolojik indeks çalışılmıştır. Topolojik indeks, bir moleküler çizgenin topolojisini tanımlamak ve bunu ilgilenilen çeşitli özelliklerle ilişkilendirmek için kullanılır. Bu topolojik indekslerin en yaygın kullanılanları derece ve uzaklık tabanlı indekslerdir. Bu makalede kimyada önemli bir yere sahip olan Gutman indeksi incelenmiştir. Gutman indeksi hem derece hem de uzaklığın aynı anda kullanıldığı, literatürde kapsamlı olarak çalışılmış iyi bilinen bir topolojik indekstir ve kimya, fizik ve diğer alanlarda birçok uygulaması vardır. Transformasyon çizgeler ise kimya, bilgisayar bilimleri ve fizik gibi alanlarda moleküler yapıları, fiziksel ağları ve algoritmaları modellemek için kullanılabilen çizgelerdir. Bu çizgeler, bir çizgenin farklı transformasyonlar altındaki özelliklerinin incelenmesini sağladıklarından önemlidir. Orijinal çizgenin simetrisi, bağlantılılığı ve diğer yapısal özellikleri, bu transformasyonlar yoluyla ortaya çıkarılabilir. Bu makalede, bazı transformasyon çizgelerin Gutman indeksi bu çizgelerin özelliklerini incelemek için kullanılabilecek yeni bir topolojik indeks sağlamak amacıyla çalışılmış ve genel formüller elde edilmiştir.

Keywords

Çizge teorisi, Transformasyon Çizge, Topolojik indeks, Gutman indeksi

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