Narumi–Katayama index of the subdivision graphs

Aşçıoğlu, Merve; Cangül, İsmaıl Nacı

doi:10.1080/16583655.2018.1474542

Cited by 6 publications

(5 citation statements)

References 12 publications

(14 reference statements)

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“…His paper explores the inverse problem concerning the sigma index, demonstrating that an even value will always be obtained for this index in any given graph. Merve and Ismail conducting a calculation of the sigma index for various graphs, adding the subdivision of the cycle graph C n , the graph of S(G), and the r-subdivision graph of S r (G) [44]. Additionally, they provide examples of well-known graph cycles.…”

Section: Reducible Sigma Indexmentioning

confidence: 99%

Analyzing the role of reducible molecular descriptors and thermodynamic aspects of anti-tuberculosis drugs via QSPR study

Alam,

Nigar,

Rasheed

et al. 2024

Front. Phys.

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Mycobacterium tuberculosis is an organism that causes tuberculosis (TB), a common infectious disease that has a high death and morbidity rate. Topological indices are mathematical tools used to describe the structural properties of molecules or networks. They provide a quantitative measure of the connectivity and complexity of a system, and play a crucial role in numerous area such as biochemistry and bioinformatics. The purpose of topological indices is to simplify complex structures into numerical values that can be easily analyzed and compared. QSPR modeling is a technique in chemistry that relates the structure of a chemical compound to its physical or chemical properties. It is used to predict properties like boiling points, solubilities, toxicities, and even biological activities of compounds. This saves time, resources, and enables researchers to make informed decisions in drug discovery, material science, and many other areas. In this study, we conducted an analysis of several drugs used for the treatment of tuberculosis. We focused on computing the reducible topological indices based on their degrees. Several techniques and approaches are employed. To perform calculations, we used edge partition methodology, analytical techniques, theoretical graph utilities, and degree counting method. Additionally, we examined six physicochemical properties of these drugs. To establish quantitative structure-property relationship models and evaluate their effectiveness, we employed linear, quadratic, and logarithmic regression analysis. By analyzing the reducible topological indices and physicochemical properties, we aimed to gain a deeper understanding of the drugs’ characteristics and their potential impact on tuberculosis treatment. This study established a significant relationship between the defined indices with two key properties: molar mass and collision cross section. The correlation coefficients for molar mass range from 0.7 to 0.9, while the collision cross section range from 0.8 to 0.9. These results demonstrate a strong association between the indices and the properties under investigation. Furthermore, it is worth noting that both molar mass and collision cross section satisfy the requirements for p-value and F-test value across all indices. This indicates the statistical significance of the observed correlations and the reliability of our findings.

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Section: Reducible Sigma Indexmentioning

confidence: 99%

Analyzing the role of reducible molecular descriptors and thermodynamic aspects of anti-tuberculosis drugs via QSPR study

Alam,

Nigar,

Rasheed

et al. 2024

Front. Phys.

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“…Subdivision graphs are used to derive various chemical and mathematical properties of complex graphs from simpler graphs. Extensive research has been done by [45] and [46] on these graphs, which facilitate the study of the chemical and physical properties of the object represented by the graph.…”

Section: Related Workmentioning

confidence: 99%

Radio Labeling of Supersub—Division of Path Graphs

Mari,

Jeyaraj

2023

IEEE Access

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Motivated by the channel assignment problem, we study the radio labeling of graphs. The radio labeling problem is an important topic in discrete mathematics due to its diverse applications, e.g., frequency assignment in mobile communication systems, signal processing, circuit and sensor network design, etc. A graph labeling problem is an assignment of labels to the vertices or edges (or both) of a graph G that satisfy a mathematical constraint. Radio labeling, a vertex labeling of graphs with non-negative integers, finds an important application in the study of radio channel assignment problems. The maximum label used in a radio labeling is called its span, and the smallest possible span of a radio labeling is called the radio number of a graph. In this area, Liu and Zhu [1] provided important results by computing the exact values of rn(G) for paths and cycles when k is equal to the diameter for certain cases. In this paper, we determine the radio number rn(G) of G where G is the supersub−division of a path P n with n ≥ 3 vertices and a complete bipartite graph K 2,α with α ∈ N.

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“…Therefore, their mathematical characteristics have been thoroughly examined. In [5] , Ascioglu and Cangul examined the forgotten topological index and the sigma ( σ ) irregularity index of r -subdivision and subdivision graphs. Réti examined lower as well as upper bounds for several irregularity indices, such as the Zagreb irregularity index, the sigma index, the forgotten topological indices, and the IRC index, etc.…”

Section: Introductionmentioning

confidence: 99%

Several Zagreb indices of power graphs of finite non-abelian groups

Ismail,

Ali,

Qasim

et al. 2023

Heliyon

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Narumi–Katayama index of the subdivision graphs

Cited by 6 publications

References 12 publications

Analyzing the role of reducible molecular descriptors and thermodynamic aspects of anti-tuberculosis drugs via QSPR study

Analyzing the role of reducible molecular descriptors and thermodynamic aspects of anti-tuberculosis drugs via QSPR study

Radio Labeling of Supersub—Division of Path Graphs

Several Zagreb indices of power graphs of finite non-abelian groups

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