Browsing by Author "Alaeiyan, Mehdi"

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Computational Techniques in Machine Learning, Fuzzy Systems, Image Processing and Signal Analysis
(Taru Publications, 2025) Farahani, Mohammad Reza; Alaeiyan, Mehdi; Ameen, Hayder Baqer; Zhang, Xiujun; Cancan, Murat; Afzal, Farkhanda
Construction of Petersen Graph Via Graph Product and Correlation of Topological Descriptors of Petersen Graph in Terms of Cyclic Graph C5
(Taylor & Francis Ltd, 2022) Waheed, Muhammad; Saleem, Umair; Cancan, Murat; Tas, Ziyattin; Alaeiyan, Mehdi; Farahani, Mohammad Reza
Graph product yields a new structure from two initial given structures. The computation of topological indices for these sophisticated structures using the graph product is a critical endeavor. Petersen graph is a structure which consists of ten vertices and fif teen edges. It is commonly used as a counter example to graph theory conjectures. In this paper, we generate simple Petersen graph by using graph product and then explicit expressions of the first and second Zagreb indices, forgotten topological index, first hyper and first reformulated Zagreb index, reduced second Zagreb index and Y-index of the Peterson graph in terms of cyclic graph C-5 are computed.
Enumeration of Spanning Trees in a Chain of Diphenylene Graphs
(Taylor & Francis Ltd, 2022) Modabish, Abdulhafid; Husin, Mohamad Nazri; Alameri, Abdu Qaid; Ahmed, Hanan; Alaeiyan, Mehdi; Farahani, Mohammed Reza; Cancan, Murat
Cheminformatics is a modern field of chemistry information science and mathematics that is very much helpful in keeping the data and getting information about chemicals. A new two-dimensional carbon known as diphenylene was identified and synthesized. It is considered one of the materials that have many applications in most fields such as catalysis. The number of spanning trees of a graph G, also known as the complexity of a graph G, denoted by tau(G), is an important, well-studied quantity in graph theory, and appears in a number of applications. In this paper, we introduce a new chemical compound that is a chain of diphenylene where any two diphenylene intersect by one edge. We derive two formulas for the number of spanning trees in a chain of diphenylene planar graphs that have connected intersection of one edge but where the diphenylenes have same sizes.
Exploring Metric Dimensions in Chemical Structures : Insights and Applications
(Taru Publications, 2025) Chaudhry, Faryal; Maktoof, Mohammed Abdul Jaleel; Mousa, Sura Hamed; Farooq, Umar; Farahani, Mohammad Reza; Alaeiyan, Mehdi; Cancan, Murat
In this article, we dive into the metric dimension of various lattice networks, focusing on Bakelite, Backbone DNA, and Polythiophene networks. The metric dimension is a crucial graph invariant that helps us understand how uniquely we can identify the vertices in a network. Our detailed analysis and calculations reveal that the metric dimension for Bakelite, Polythiophene, and Backbone DNA networks is consistently two. This means that, within these lattice structures, a simple pair of vertices is enough to pinpoint the location of all other vertices. These insights shed light on the structural properties of these molecular networks and could have practical implications for areas like biological systems and organic electronics. Plus, this study sets the stage for future research in graph theory and the understanding of molecular structures.
On Metric Dimension of Circumcoronene Series of Benzenoid Networks
(Taru Publications, 2025) Chaudhry, Faryal; Abbas, Azhar Ali; Maktoof, Mohammed Abdul Jaleel; Farooq, Umar; Farahani, Mohammad Reza; Alaeiyan, Mehdi; Cancan, Murat
In molecular topology and chemistry, resolving sets and metric bases are essential concepts. They have numerous applications in computer science, artificial intelligence, chemistry, pharmacy, traffic networking, mathematical modeling, and programming. Adivision S of the vertex set chi of a linked graph G is said to resolve G if eachpoint of G can be represented from its neighborhood in S. A metric dimension of a graph is the number of the smallest resolving set, also known as the metric basis of the graph.In the current research we will determine the metric dimension and metric basis of the circumcoronene series CS of benzenoid Hk for k >= 1. We prove that a set with three vertices is required to resolve this graph, and therefore, its metric dimension is 3.
On Sombor Indices of Line Graph of Silicate Carbide Si2c3-I[p,q]
(Taylor & Francis Ltd, 2022) Asif, Fatima; Zahid, Zohaib; Husin, Mohamad Nazri; Cancan, Murat; Tas, Ziyattin; Alaeiyan, Mehdi; Farahani, Moahmmad Reza
Topological indices are numerical parameters associated with underlying topology of a molecular structure. They are correlated with several physio-chemical properties of chemical compounds. Recently, Euclidean metric based topological index has been introduced named as Sombor index. Therefore, in this article, we will discuss combinatorial aspects and compute Sombor index, average Sombor index and the reduced Sombor index of line graph of silicate carbides Si2C3-I[p, q].
On Topological Indices of Certain Families of Graphs
(Iop Publishing Ltd, 2025) Imran, Muhammad; Farahani, Muhammad Reza; Cancan, Murat; Alaeiyan, Mehdi; Akguel, Ali
The aim of this paper is to compute topological indices such as general randic index, general sumconnectivity index, atom bond connectivity index, geometric arithmetic index, forgotten index,firstzagreb index, second zagreb index,first multiple zagreb index, second multiple zagreb index and hyperzagreb index of different families of graphs.
On Van, R and S Topological Properties of the Sierpinski Triangle Networks
(Sami Publishing Co-spc, 2020) Ediz, Suleyman; Alaeiyan, Mehdi; Farahani, Mohammad Reza; Cancan, Murat
A topological index-a numerical quantity derived from the graph of a chemical network-is used for modelling the mathematical, chemical and physical properties of these networks and chemicals. The topological properties of the Sierpinski triangle has been newly studied in chemical graph theory. In this study we defined novel Van, R and S degree concepts as well as novel Van, R and S topological indices, and computed these topological indices for the Sierpinski triangle network. The closed formulas of these novel topological indices for the Sierpinski triangle network were presented.
On Ve-Degree Molecular Properties of Copper Oxide
(Analytic Publ Co, 2020) Cancan, Murat; Ediz, Suleyman; Alaeiyan, Mehdi; Farahani, Mohammad Reza
Mathematical topological characterization of chemical graphs gives information about some physical properties of molecules. Classical degree based topological indices of copper oxide have been recently calculated. Ve-degree and Ev-degree based topological indices have been newly defined in graph theory. In this study we investigate ve-degree topological properties of copper oxide. We calculate ve-degree Zagreb and Randic indices of copper oxide.
Resistance Distance in Some Classes of Rooted Product Graphs Obtained by Laplacian Generalized Inverse Method
(Taylor & Francis Ltd, 2021) Sardar, Muhammad Shoaib; Alaeiyan, Mehdi; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
In mathematics, a graph product is a binary operation on a graph. Graph products have been extensively researched and have many important applications in many fields. Here we discuss one graph-theoretical product. Let H be a labeled graph on n vertices and let G be a rooted graph. Denote by H G the graph obtained by identifying the root vertex of the ith copy of G with the ith vertex of H. H G is called by the rooted product of H by G [C. Godsil, B. D. McKay, A new graph product and its spectrum, Bull. Aust. Math. Soc. 18 (1978)]. The resistance distance between two vertices i and j of a graph G is defined as the effective resistance between the two vertices when a unit resistor replaces each edge of G. Let H-k;n, C-m, S-k, P-k and K-u be the Harary, cycle, star, path and complete graphs respectively. In this paper, the symmetric {1}-inverses of Laplacian matrices for graphs (H-k;n circle C-m), (H-k;n circle K-u), (C-n circle S-k) and (C-n circle P-k) are studied, based on which the resistance distances of any two vertices in these graphs can be obtained. In addition, some examples are provided as applications that illustrate the functionality of the suggested method.
The Study of the B-Choromatic Number of Some Classes of Fractal Graphs
(Taru Publications, 2022) Sattar, Tayyiba; Sardar, Muhammad Shoaib; Alaeiyan, Mehdi; Farahani, Moahmmad Reza; Cancan, Murat; Tas, Ziyattin
In graph coloring, labels are assigned to graph elements according to certain constraints. Colors are a special case of graph labeling as well as in practical applications, graph coloring also poses some theoretical challenges. A topic related to graph coloring will be discussed in this study, i.e., b-chromatic number. In proper coloring, edges, vertices, or both of them are colored so that they are distinct from one another. A b-coloring of m colors of a graph G is similar to proper coloring in which at least one vertex from each color class is connected to (m-1) other colors. The b-chromatic number of a graph G is the greatest positive number k such that G admits a b-coloring with k colors and is represented by phi(G). Fractals are geometric objects that are self-similar at multiple scales and their geometric measurements are different from fractal measurements. In this paper, we will evaluate the b-chromatic number of Fractal type graphs, i.e., Sierpinski network S(n; Kk) (where Kk is a complete graph of order k) and Sierpinski gasket network S(n). Firstly, we will compute the b-chromatic number of S(n; K3), S(n; K4) and S(n; K5) for n >= 2. After that, we will generalize the result for the Sierpinski network of complete graph Kk. In addition, we will also determine the b-choromatic number of Sierpinski gasket graph S(n). As an application, we will also determine the b-chromatic number of Sierpinski graph of house graph.
Ve-Degree and Ev-Degree Topological Analysis of Some Anticancer Drugs
(Sami Publishing Co-spc, 2020) Ediz, Suleyman; Cancan, Murat; Alaeiyan, Mehdi; Farahani, Mohammad Reza
Computing topological indices of drug structures provides the chemical information about the underlying topology of the drug's structures. Novel anticancer drug studies have been conducting by researches to design and produce ideal drugs. Chemical properties of these new drug candidates investigated using the simulation methods. Topological indices also have been used to investigate the chemical properties of some drug structures. Ve-degree and Ev-degree topological indices have been defined recently in chemical graph theory. In this study we evaluated the ev-degree and ye-degree topological indices of some newly defined anticancer drug candidates which are based on alkylating agent.