M. C. Shanmukha¹, Sokjoon Lee^2,*, A. Usha³, K. C. Shilpa⁴, Muhammad Azeem⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.1, pp. 939-964, 2023, DOI:10.32604/cmes.2023.027254

Abstract Graph theory plays a significant role in the applications of chemistry, pharmacy, communication, maps, and aeronautical fields. The molecules of chemical compounds are modelled as a graph to study the properties of the compounds. The geometric structure of the compound relates to a few physical properties such as boiling point, enthalpy, π-electron energy, molecular weight. The article aims to determine the practical application of graph theory by solving one of the interdisciplinary problems describing the structures of benzenoid hydrocarbons and graphenylene. The topological index is an invariant of a molecular graph associated with the chemical structure, which shows the correlation… More >

Yonghong Liu¹, Muhammad Waheed², Umair Saleem³, Muhammad Kamran Jamil^4,*, Muhammad Naveed⁵, Mohammad Reza Farahani⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1899-1916, 2023, DOI:10.32604/cmes.2023.025071

Abstract L-valine is a glycogen-type amino acid regarded among the necessary mammalian amino acids. This is an amino acid that is essential for protein synthesis. N-salicylidene-L-valine is gaining a lot of attention because of its unique structure and increased catalytic and cytotoxic activity. We explore the chain of supramolecular dialkyltin N-salicylidene-L-valine complexes 2, 3, and 4 to learn more about this structure and its features regarding topological indices. We computed the first and second Randić index, harmonic index, sum-connectivity index, atom-bond-connectivity index, geometric arithmetic index and reduced reciprocal Randić index of Supramolecular Chain of Different Complexes of N-Salicylidene-L-Valine. Furthermore, we present… More >

Wenhu Wang^1,2,3, Hibba Arshad⁴, Asfand Fahad^4,*, Imran Javaid⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1685-1699, 2023, DOI:10.32604/cmes.2022.023563

Abstract One of the most recent developments in the field of graph theory is the analysis of networks such as Butterfly networks, Benes networks, Interconnection networks, and David-derived networks using graph theoretic parameters. The topological indices (TIs) have been widely used as graph invariants among various graph theoretic tools. Quantitative structure activity relationships (QSAR) and quantitative structure property relationships (QSPR) need the use of TIs. Different structure-based parameters, such as the degree and distance of vertices in graphs, contribute to the determination of the values of TIs. Among other recently introduced novelties, the classes of ev-degree and ve-degree dependent TIs have… More >

Jung Rye Lee¹, Aftab Hussain², Asfand Fahad³, Ali Raza³, Muhammad Imran Qureshi^3,*, Abid Mahboob⁴, Choonkil Park⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.2, pp. 871-885, 2022, DOI:10.32604/cmes.2022.016836

Abstract In quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies, computation of topological indices is a vital tool to predict biochemical and physio-chemical properties of chemical structures. Numerous topological indices have been inaugurated to describe different topological features. The ev and ve-degree are recently introduced novelties, having stronger prediction ability. In this article, we derive formulae of the ev-degree and ve-degree based topological indices for chemical structure of Si₂C₃ − I[a,b]. More >

Sadia Husain¹, Muhammad Imran^2,*, Ali Ahmad¹, Yasir Ahmad¹, Kashif Elahi³

CMC-Computers, Materials & Continua, Vol.70, No.2, pp. 3433-3447, 2022, DOI:10.32604/cmc.2022.020384

Abstract The Cellular Neural Network (CNN) has various parallel processing applications, image processing, non-linear processing, geometric maps, high-speed computations. It is an analog paradigm, consists of an array of cells that are interconnected locally. Cells can be arranged in different configurations. Each cell has an input, a state, and an output. The cellular neural network allows cells to communicate with the neighbor cells only. It can be represented graphically; cells will represent by vertices and their interconnections will represent by edges. In chemical graph theory, topological descriptors are used to study graph structure and their biological activities. It is a single… More >

Sadia Husain¹, Fouad A. Abolaban², Ali Ahmad¹, Muhammad Ahsan Asim¹, Yasir Ahmad¹

Computer Systems Science and Engineering, Vol.40, No.3, pp. 835-850, 2022, DOI:10.32604/csse.2022.018534

Abstract Due to the combinatorial nature of graphs they are used easily in pure sciences and social sciences. The dynamical arrangement of vertices and their associated edges make them flexible (like liquid) to attain the shape of any physical structure or phenomenon easily. In the field of ICT they are used to reflect distributed component and communication among them. Mathematical chemistry is another interesting domain of applied mathematics that endeavors to display the structure of compounds that are formed in result of chemical reactions. This area attracts the researchers due to its applications in theoretical and organic chemistry. It also inspires… More >

Muhammad Ibrahim^1,*, Sadia Husain², Nida Zahra¹, Ali Ahmad²

Computer Systems Science and Engineering, Vol.40, No.1, pp. 247-258, 2022, DOI:10.32604/csse.2022.018227

Abstract Chemical graph theory is a branch of mathematics which combines graph theory and chemistry. Chemical reaction network theory is a territory of applied mathematics that endeavors to display the conduct of genuine compound frameworks. It pulled the research community due to its applications in theoretical and organic chemistry since 1960. Additionally, it also increases the interest the mathematicians due to the interesting mathematical structures and problems are involved. The structure of an interconnection network can be represented by a graph. In the network, vertices represent the processor nodes and edges represent the links between the processor nodes. Graph invariants play… More >

Ali N. A. Koam¹, Ali Ahmad^2,*, M. F. Nadeem³

Computer Systems Science and Engineering, Vol.36, No.2, pp. 293-306, 2021, DOI:10.32604/csse.2021.014896

Abstract A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena. The structure of an interconnection network can be represented by a graph. In the network, vertices represent the processor nodes and edges represent the links between the processor nodes. Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks. A topological descriptor is a numerical total related to a structure that portray the topology of structure and is invariant under structure automorphism.… More >

Raghisa Khalid¹, Nazeran Idrees^1,*, Muhammad Jawwad Saif²

CMC-Computers, Materials & Continua, Vol.60, No.1, pp. 41-54, 2019, DOI:10.32604/cmc.2019.06554

Abstract Degree based topological indices are being widely used in computer-aided modeling, structural activity relations, and drug designing to predict the underlying topological properties of networks and graphs. In this work, we compute the certain important degree based topological indices like Randic index, sum connectivity index, ABC index, ABC₄ index, GA index and GA₅ index of Book graph B_n and Stacked book graph B_m,n. The results are analyzed by using edge partition, and the general formulas are derived for the above-mentioned families of graphs. More >

Murat Cancan^{1, *}

CMC-Computers, Materials & Continua, Vol.59, No.3, pp. 777-786, 2019, DOI:10.32604/cmc.2019.06596

Abstract Topological indices enable to gather information for the underlying topology of chemical structures and networks. Novel harmonic indices have been defined recently. All degree based topological indices are defined by using the classical degree concept. Recently two novel degree concept have been defined in graph theory: ve-degree and ev-degree. Ve-degree Zagreb indices have been defined by using ve-degree concept. The prediction power of the ve-degree Zagreb indices is stronger than the classical Zagreb indices. Dominating oxide, silicate and oxygen networks are important network models in view of chemistry, physics and information science. Physical and mathematical properties of dominating oxide, silicate… More >