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Article
Biochemistry & Molecular Biology
Jun Yang et al.
Summary: A topological index is a real number that describes the relationship between chemical structures and their properties under graph isomorphism. This article focuses on calculating the neighbourhood sum degree-based M-polynomial and entropy measures for graphene, graphyne, and graphdiyne structures. The derived analytical expressions for these indices provide insights for theoretical chemists to study these unique structures further.
Article
Physics, Multidisciplinary
Asad Ullah et al.
Summary: Mathematical chemistry uses mathematics to solve chemistry problems. This paper calculates and derives closed formulas for the first and second Zagreb connection indices of triangular chain structures. By using these formulas and obtained numerical results, the physicochemical properties of these structures can be easily investigated.
Article
Biochemistry & Molecular Biology
Asad Ullah et al.
Summary: Quantitative structure-activity relationship (QSAR) is a method that correlates the biological structural features (topological indices) with pharmacological activity. Topological indices are numerical functions used to predict the growth rate of microorganisms in biological networks. Theoretical assessment of microorganisms helps in vaccine design and discovery by understanding their mechanism of actions. This article investigates the biological properties of two important biological networks (hypertree and its corona product) by obtaining novel topological features and deriving closed formulas for them.
JOURNAL OF BIOMOLECULAR STRUCTURE & DYNAMICS
(2023)
Article
Chemistry, Physical
Abdul Hakeem et al.
Summary: Topological indices are mathematical tools used to characterize the molecular structure of a compound and predict its properties. In this study, a graph theory-based technique is used to model the molecular topology of ?-Graphyne and Zigzag graphyne nanoribbon, and mathematical expressions for some essential degree-based molecular descriptors are derived. These computed indices are illustrated with graphical representations and numerical tables.
Article
Chemistry, Organic
Shahid Zaman et al.
Summary: Topological indices have multiple biological applications in the treatment of blood cancer, including predicting drug efficacy and toxicity, as well as aiding in drug discovery and design. This article examines the use of topological indices in predicting the properties of novel drugs used in blood cancer treatment, such as boiling point, flash point, molar volume, molecular weight, and complexity. The results show the potential of topological indices as a tool for drug discovery and design in cancer treatment.
POLYCYCLIC AROMATIC COMPOUNDS
(2023)
Article
Multidisciplinary Sciences
Muhammad Usman Ghani et al.
Summary: This article aims to encourage original research on topological graph indices for the drugs azacitidine, decitabine, and guadecitabine, and to investigate the genesis of symmetry in actual networks. These hypomethylating drugs are used to treat patients with higher-risk myelodysplastic syndromes, chronic myelomonocytic leukemia, and acute myeloid leukemia who are not candidates for intense regimens.
Article
Mathematics
Muhammad Azeem et al.
Summary: The act of locating the exact position of nodes in a network is called network localization. In this study, the localization of a generalized hexagonal cellular network was conducted, and the exact locating number for this network was determined and proven. Furthermore, the generalized version of the locating set and locating number was also discussed.
Article
Chemistry, Physical
Asad Ullah et al.
Summary: Bioconjugate networks are formed by connecting different molecules or particles through covalent or non-covalent interactions, and they have various applications in biology and medicine. Understanding the structure-property relationships of these networks is important for developing more effective antibiotics.
EUROPEAN PHYSICAL JOURNAL E
(2023)
Article
Multidisciplinary Sciences
Asad Ullah et al.
Summary: Topological indices are used to predict physical features related to bioactivities and chemical reactivity in certain networks. 2D nanotubes are thin nanomaterials with excellent chemical functionality and anisotropy, making them ideal for surface interactions. This paper derives closed formulae for important neighborhood-based irregular topological indices of 2D nanotubes and performs a comparative analysis of the computed indices.
SCIENTIFIC REPORTS
(2023)
Article
Chemistry, Organic
Xiujun Zhang et al.
Summary: Nanostructures are important and extensively studied compounds in chemical science. The computation and study of topological indices for these structures are crucial in the field of nanotechnology. This paper computes topological indices based on ev-degree and ve-degree for carbon nanosheets, providing a foundation for the study of structure-property relationships in carbon nanotube compounds.
POLYCYCLIC AROMATIC COMPOUNDS
(2022)
Article
Biochemical Research Methods
Xiujun Zhang et al.
Summary: Cerium oxide nanoparticles are widely used as catalysts in industry, leading to their significant presence in water systems. This study focuses on analyzing the crystal structure of Ceria Oxide and calculating the Heat of Formation and Entropy using degree-based topological indices. Various topological indices were computed and discussed in relation to the physical properties of the cuprite CeO2 nanocrystal, showing potential for nanoceria engineering.
COMBINATORIAL CHEMISTRY & HIGH THROUGHPUT SCREENING
(2022)
Article
Biochemical Research Methods
Jia-Bao Liu et al.
Summary: This article discusses the importance of the concepts of partition and resolving sets in various fields of engineering, chemistry, and computer science. It explores the problem of partition dimension in graphs and provides bounds for convex polytopes. The contribution of the article lies in providing bounds for the complexity of computing the exact partition dimension.
COMBINATORIAL CHEMISTRY & HIGH THROUGHPUT SCREENING
(2022)
Article
Multidisciplinary Sciences
Ashequr Rahman Milon et al.
Summary: Complex networks and Mobius structures are difficult to decode and understand. The identification of each vertex is also challenging. Resolvability parameters play a crucial role in controlling or accessing the vertices, making it easier to access each vertex.
JOURNAL OF KING SAUD UNIVERSITY SCIENCE
(2022)
Article
Engineering, Multidisciplinary
Mohamad Nazri Husin et al.
Summary: This paper presents different versions of the ABC index in chemical graph theory and numerical simulations of novel families of atom-bond connectivity indices. These indices are important for QSAR and QSPR studies in chemistry.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2022)
Article
Mathematics, Applied
Abdulhafid Modabish et al.
Summary: Cheminformatics is a helpful field in chemistry information science and mathematics, which focuses on maintaining data and obtaining information about chemicals. A new two-dimensional carbon material called diphenylene has been synthesized, and it is considered to have various applications, particularly in catalysis. The number of spanning trees in a graph, also known as the graph's complexity, is an important and well-studied quantity in graph theory. The paper introduces a new chemical compound consisting of a chain of diphenylene, where any two diphenylene intersect by one edge. It derives two formulas for calculating the number of spanning trees in a chain of diphenylene planar graphs with connected intersection of one edge and diphenylenes of the same size.
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY
(2022)
Article
Mathematics, Applied
Muhammad Faisal Nadeem et al.
Summary: This article investigates the locating number of a newly designed hexagonal Moebius ladder network, which refers to the minimum number of nodes in the locating/resolving set. By selecting several nodes, the exact location of a specific node can be obtained in the network.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Mathematics
Ali N. A. Koam et al.
Summary: This study discusses the concepts of vertices, edges, and degree in a network, highlighting the importance of degree appropriation for revealing global network characteristics. Network theory is utilized in various fields such as sociology, medicine, and engineering, with different significant networks being identified.
JOURNAL OF MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
Muhammad Azeem et al.
Summary: This article explores some resolvability parameters of polycyclic aromatic hydrocarbons, such as metric dimension, edge metric dimension, and generalizations. Shaping the entire structure into a novel form through resolvability parameters aids in comprehension and manipulation of the structure.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Computer Science, Information Systems
Ayesha Shabbir et al.
Summary: The production of low-cost, small in size, and high in efficiency objects is a popular research topic across various scientific fields, with a particular focus on engineering. Nanotechnology plays a significant role in achieving these goals. This study utilizes the Partition Dimension tool to uniquely identify each atom in a tri-hexagonal lattice of the alpha-boron nanotube.
Article
Mathematics, Applied
Sourav Mondal et al.
INTERNATIONAL JOURNAL OF MATHEMATICS FOR INDUSTRY
(2019)
Article
Biochemistry & Molecular Biology
Xiujun Zhang et al.
Article
Multidisciplinary Sciences
Xiujun Zhang et al.
Proceedings Paper
Mathematics, Applied
Mohamad Nazri Husin et al.
1ST INTERNATIONAL CONFERENCE OF COMBINATORICS, GRAPH THEORY, AND NETWORK TOPOLOGY
(2018)
Article
Wei Gao et al.
Journal of Computational and Theoretical Nanoscience
(2017)
Article
Yun Liu et al.
Journal of Computational and Theoretical Nanoscience
(2017)
Article
Mathematics
V. S. Shigehalli et al.
JOURNAL OF MATHEMATICS
(2016)
Article
Nanoscience & Nanotechnology
G. Sridhara et al.
JOURNAL OF NANOMATERIALS
(2015)
