Browsing by Author "Cancan, M."

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Analyzing the Boron Triangular Nanotube Through Topological Indices Via M-Polynomial
(Taylor and Francis Ltd., 2021) Hussain, S.; Afzal, F.; Afzal, D.; Cancan, M.; Ediz, S.; Farahani, M.R.
he current discovery of different types of nanostructures has inspired the researcher to study the applications of these structures in different fields. In this study, we have analyzed the boron triangular nanotube through topological indices. M-polynomial of a boron triangular nanotube has the capability to recover the topological indices which are dependent on the degree of the vertex. We have presented the results in graphical form. © 2021 Taru Publications.
Browder's Fixed Point Theorem and Some Interesting Results in Intuitionistic Fuzzy Normed Spaces
(Hindawi Publishing Corporation, 2010) Cancan, M.
We define and study Browder's fixed point theorem and relation between an intuitionistic fuzzy convex normed space and a strong intuitionistic fuzzy uniformly convex normed space. Also, we give an example to show that uniformly convex normed space does not imply strongly intuitionistic fuzzy uniformly convex.
Choosing Friends in Everyday Life by Using Graph Theory
(Charles Babbage Research Centre, 2024) Mughal, A.A.; Jamil, R.N.; Farahani, M.R.; Alaeiyan, M.; Cancan, M.
Graph theory is playing vital role in almost every field of our routine life. You make a conference call with your friends by using vertices (yourself and your friends) and edges (network connection). You construct a printed grid floor with different faces in your home by the help of graph theory. Authors in this study are using labelling of graphs and applying it in choosing best friends around you. The helping graphs in this article will be plane graphs which will be labelling under k−labelling M of kind (λ, µ, ν). This study can be applied in many fields of everyday life. © 2024 the Author(s), licensee Combinatorial Press.
Computing Metric Dimension of Two Types of Claw-Free Cubic Graphs With Applications
(Charles Babbage Research Centre, 2024) Sardar, M.S.; Xu, S.-J.; Cancan, M.; Farahani, M.R.; Alaeiyan, M.; Patil, S.V.
Consider the simple connected graph G with vertex set V(G) and edge set E(G). A graph G can be resolved by R if each vertex’s representation of distances to the other vertices in R uniquely identifies it. The minimum cardinality of the set R is the metric dimension of G. The length of the shortest path between any two vertices, x, y in V(G), is signified by the distance symbol d(x, y). An ordered k-tuple r(x/R) = (d(x, z1), d(x, z2), ..., d(x, zk)) represents representation of x with respect to R for an ordered subset R = {z1, z2, z3..., zk} of vertices and vertex x in a connected graph. Metric dimension is used in a wide range of contexts where connection, distance, and connectedness are essential factors. It facilitates understanding the structure and dynamics of complex networks and problems relating to robotics network design, navigation, optimization, and facility location. Robots can optimize their localization and navigation methods using a small number of reference sites due to the pertinent idea of metric dimension. As a result, many robotic applications, such as collaborative robotics, autonomous navigation, and environment mapping, are more accurate, efficient, and resilient. A claw-free cubic graph (CCG) is one in which no induced subgraph is a claw. CCG proves helpful in various fields, including optimization, network design, and algorithm development. They offer intriguing structural and algorithmic properties. Developing algorithms and results for claw-free graphs frequently has applications in solving of challenging real-world situations. The metric dimension of a couple of claw-free cubic graphs (CCG), a string of diamonds (SOD), and a ring of diamonds (ROD) will be determined in this work. © 2024 the Author(s), licensee Combinatorial Press.
Degree-Based Topological Indices and Polynomials of Cellulose
(Abdus Salam School of mathematical Sciences, 2021) Khalaf, A.J.M.; Shanmukha, M.C.; Usha, A.; Shilpa, K.C.; Cancan, M.
This work attempts to compute cellulose's chemical structure using topological indices based on the degree and its neighbourhood. The study of graphs using chemistry attracts a lot of researchers globally because of its enormous applications. One such application is discussed in this work, where the structure of cellulose is considered for which the computation of topological indices and analysis of the same are carried out. A polymer is a repeated chain of the same molecule stuck together. Glucose is a natural polymer also called, Polysaccharide. The diet of the humans include fibre which contains cellulose but direct consumption of the same may not be digestible by them. © 2021. All Rights Reserved.
Distance and Degree Based Topological Polynomial and Indices of X-Level Wheel Graph
(Abdus Salam School of mathematical Sciences, 2021) Hasan, A.; Qasmi, M.H.A.; Alsinai, A.; Alaeiyan, M.; Farahani, M.R.; Cancan, M.
In this paper we discussed the partitioning of the wheel graph and we calculate the M-polynomial, Hosoya polynomial, Harary polynomial, Schultz polynomial, Modified Schultz polynomial, Eccentric connectivity polynomial, Modified Wiener index, Modified Hyper Wiener index, Generalized Harary index, Multiplicative Wiener index, Schultz index, Modified Schultz index, Eccentric connectivity index and also derived the Randic index, Generalized Randic index, First Zagreb, Second Zagreb, Second Modified Zagreb, General Randic and Inverse General Randic, Harmonic, Symmetric Division and Inverse Sum index of generalized wheel networks Wx,y. © 2021
Distance and Eccentricity Based Polynomials and Indices of M-Level Wheel Graph
(Universidad Catolica del Norte, 2020) Cancan, M.; Hussain, M.; Ahmad, H.
Distance and degree based topological polynomial and indices ofmolecular graphs have various applications in chemistry, computer networking and pharmacy. In this paper, we give hosoya polynomial, Harary polynomial, Schultz polynomial, modified Schultz polynomial, eccentric connectivity polynomial, modified Wiener index, modified hyper Wiener index, generalized Harary index, multiplicative Wiener index, Schultz index, modified Schultz index, eccentric connectivity index of generalized wheel networks Wn, m. We also give pictorial representation of computed topological polynomials and indices on the involved parameters m and n. © 2020 Murat Cancan, Muhammad Hussain and Haseeb Ahmad.
Domination Version: Sombor Index of Graphs and Its Significance in Predicting Physicochemical Properties of Butane Derivatives
(Sami Publishing Company, 2023) Shashidhara, A.A.; Ahmed, H.; Soner Nandappa, D.; Cancan, M.
In graph theory, topological indices and domination parameters are essential topics. A dominating set for a graph G=(V(G),E(G)) is a subset D of V(G) such that every vertex not in D is adjacent to at least one vertex of D introduced novel topological indices known as domination topological indices. In this research work, we found exact values to determine Sombor index of some families of graphs including the join and corona product. Some bounds for these new topological indices were also found. Likewise, we defined the significance of the Sombor index in predicting the physicochemical properties of butane derivatives. Copyright © 2023 by SPC.
Edge Irregularity Strength of Certain Families of Comb Graph
(Universidad Catolica del Norte, 2020) Zhang, X.; Cancan, M.; Nadeem, M.F.; Imran, M.
Edge irregular mapping or vertex mapping h: V (U)-→ l, 2, 3, 4,..., s is a mapping of vertices in such a way that all edges have distinct weights. We evaluate weight of any edge by using equation wth(cd) = h(c)+h(d), \∀c, d∈ V (U) and \∀cd ∈ E(U). Edge irregularity strength denoted by es(U) is a minimum positive integer use to label vertices to form edge irregular labeling. In this paper, we find exact value of edge irregularity strength of different families of comb graph. © 2020 Xiujun Zhang, Murat Cancan, Muhammad Faisal Nadeem, and Muhammad Imran.
Employing Machine Learning To Analyze Nsaids Drug Similarity Via Sombor Invariants
(Utilitas Mathematica Publishing Inc., 2024) Virk, A.U.R.; Ahmed, I.; Cancan, M.
This study introduces a novel approach to investigating Sombor indices and applying machine learning methods to assess the similarity of non-steroidal anti-in ammatory drugs (NSAIDs). The research aims to predict the structural similarities of nine commonly prescribed NSAIDs using a machine learning technique, speci cally a linear regression model. Initially, Sombor indices are calculated for nine different NSAID drugs, providing numerical representations of their molecular structures. These indices are then used as features in a linear regression model trained to predict the similarity values of drug combinations. The model's prediction performance is evaluated by comparing the predicted similarity values with the actual similarity values. Python programming is employed to verify accuracy and conduct error analysis. © 2024 The Author(s). Published by Combinatorial Press.
Fault Tolerant Metric Dimension of Arithmetic Graphs
(Charles Babbage Research Centre, 2024) Sardar, M.S.; Rasheed, K.; Cancan, M.; Farahani, M.R.; Alaeiyan, M.; Patil, S.V.
For a graph G, two vertices x, y ∈ G are said to be resolved by a vertex s ∈ G if d(x|s), d(y|s), where d(x|s) denotes the distance between x and s. The minimum cardinality of such a resolving set R in G is called the metric dimension. A resolving set R is said to be fault-tolerant if, for every p ∈ R, the set R − p preserves the property of being a resolving set. The fault-tolerant metric dimension of G is the minimal possible order of a fault-tolerant resolving set. The concept of metric dimension has wide applications in areas where connection, distance, and network connectivity are critical. This includes understanding the structure and dynamics of complex networks, as well as addressing problems in robotic network design, navigation, optimization, and facility placement. By utilizing the concept of metric dimension, robots can optimize their methods for localization and navigation using a limited number of reference points. As a result, various applications in robotics, such as collaborative robotics, autonomous navigation, and environment mapping, have become more precise, efficient, and resilient. The arithmetic graph Al is defined as the graph where the vertex set is the set of all divisors of a composite number l, where l = pγ11 pη22 · · · pαnn and the pi’s are distinct primes with pi ≥ 2. Two distinct divisors x and y of l are said to have the same parity if they share the same prime factors (e.g., x = p1p2 and y = p21p32 have the same parity). Furthermore, two distinct vertices x, y ∈ Al are adjacent if and only if they have different parity and gcd(x, y) = pi (greatest common divisor) for some i ∈ {1, 2, . . ., t}. This article focuses on the investigation of the arithmetic graph of a composite number l, referred to throughout as Al. In this study, we compute the fault-tolerant resolving set and the fault-tolerant metric dimension of the arithmetic graph Al, where l is a composite number. © 2024 the Author(s), licensee Combinatorial Press.
Foreword
(Taru Publications, 2025) Farahani, M.R.; Alaeiyan, M.; Ameen, H.B.; Zhang, X.; Cancan, M.; Afzal, F.
Further Results on Edge Irregularity Strength of Some Graphs
(Universidad Catolica del Norte, 2024) Imran, M.; Cancan, M.; Nadeem, M.F.; Ali, Y.
The focal point of this paper is to ascertain the precise value of edge irregularity strength of various finite, simple, undirected and captivating graphs, including the splitting graph, shadow graph, jewel graph, jellyfish graph and m copies of 4-pan graph. © (2024), (Universidad Catolica del Norte). All rights reserved.
Intuitionistic Fuzzy Stability of a Jensen Functional Equation Via Fixed Point Technique
(Pergamon-elsevier Science Ltd, 2011) Mohiuddine, S. A.; Cancan, M.; Sevli, H.
The object of this paper is to determine Hyers-Ulam-Rassias stability concerning the Jensen functional equation in intuitionistic fuzzy normed space (IFNS) by using the fixed point method. Further, we establish stability of the Cauchy functional equation in IFNS. (C) 2011 Elsevier Ltd. All rights reserved.
M-Polynomial and Topological Indices of Benzene Ring Embedded in P-Type Surface Network
(Universidad Catolica del Norte, 2020) Cancan, M.; Ediz, S.; Baig, A.Q.; Khalid, W.
The representation of chemical compounds and chemical networks with the M-polynomials is a new idea and it gives nice and good results of the topological indices. These results are used to correlate the chemical compounds and chemical networks with their chemical properties and bioactivities. Particular attention is paid to the derivation of the M polynomia-for the benzene ring embedded in the P-type surface network in 2D. Furthermore, the topological indices based on the degrees are also derived by using the general form of M-polynomial of benzene ring embedded in the P-type surface network BR(m, n). In the end, the graphical representation and comparison of the M-polynomial and the topological indices of benzene ring embedded in P-type surface network in 2D are described. © 2020 Murat Cancan, Siileyman Ediz, Abdul Qudair Baig, and Waqas Khalid.
Mathematical Modeling and Estimation of Physicochemical Properties of Non-Steroidal Anti-Inflammatory Drugs Via an Innovative Approach of Biquadratic Regression Analysis
(Bentham Science Publishers, 2025) Khan, A.R.; Ullah, Z.; Qadir, F.; Salman, M.; Cancan, M.
Background: In mathematical chemistry (particularly in chemical graph theory), reverse degree-based topological indices provide good correlations with respect to both mathematical and chemical perspectives for the prediction of biological activities of diverse nature with a variety of relationships between physical, chemical, and thermodynamic parameters. Objective: The main aim of this study is to provide the reverse degree-based graph polynomial, along with its corresponding topological indices. The objective of this methodology is to estimate the physical and chemical properties of specific molecular parameters through an innovative approach, biquadratic regression analysis. Methods: Reverse degree-based graph polynomials are utilized to compute various reverse degree-based topological indices. The outcomes of this study are utilized to perform an innovative approach, biquadratic regression analysis, to estimate the various physicochemical properties of NSAID drugs. This approach provides the best approximations for the said properties. Results: The main focus of the research is the connection between changes in topological indices and physical characteristics. Based on these findings, this article may aid chemists and pharmaceutical industry professionals in the development of novel pharmaceuticals. A similar relationship can be found between topological indices and the physical characteristics of newly discovered medications for treating specific diseases to assess the physical characteristics of those medications. This study provides a QSPR experiment using biquadratic regression models to yield greater estimates for the properties of the NSAIDs. Conclusion: Through the utilization of Biquadratic regression models, we have discovered that the indices that we have presented have a close relationship with both the chemical and physical parameters. © 2025 Bentham Science Publishers.
Molecular Descriptors of Certain Class of Carbon Nanocone Networks Through Quotient Graph Approach
(Charles Babbage Research Centre, 2024) Ragoub, L.; Baby, A.; Xavier, D.A.; Ghani, M.U.; Varghese, E.S.; Theertha Nair, A.; Cancan, M.
Nanoparticles have potential applications in a wide range of fields, including electronics, medicine and material research, because of their remarkable and exceptional attributes. Carbon nanocones are planar carbon networks with mostly hexagonal faces and a few non-hexagonal faces (mostly pentagons) in the core. Two types of nanocone configurations are possible: symmetric and asymmetric, depending on where the pentagons are positioned within the structure. In addition to being a good substitute for carbon nanotubes, carbon nanocones have made an identity for themselves in a number of fields, including biosensing, electrochemical sensing, biofuel cells, supercapacitors, gas storage devices, and biomedical applications. Their astonishing chemical and physical attributes have made them well-known and widely accepted in the fields of condensed matter physics, chemistry, material science, and nanotechnology. Mathematical and chemical breakthroughs were made possible by the concept of modeling a chemical structure as a chemical graph and quantitatively analyzing the related graph using molecular descriptors. Molecular descriptors are useful in many areas of chemistry, biology, computer science, and other sciences because they allow for the analysis of chemical structures without the need for experiments. In this work, the quotient graph approach is used to establish the distance based descriptors of symmetrically configured two-pentagonal and three-pentagonal carbon nanocones. © 2024 the Author(s).
Molecular Descriptors of Certain Otis Interconnection Networks
(Universidad Catolica del Norte, 2020) Cancan, M.; Ahmad, I.; Ahmad, S.
Network theory as an important role in the field of electronic and electrical engineering, for example, in signal processing, networking, communication theory, etc. The branch of mathematics known as Graph theory found remarkable applications in this area of study. A topological index (TI) is a real number attached with graph networks and correlates the chemical networks with many physical and chemical properties and chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has received considerable attention in recent years and has a special place among real world architectures for parallel and distributed systems. In this report, we compute redefined first, second and third Zagreb indices of OTIS swapped and OTIS biswapped networks. We also compute some Zagreb polynomials of understudy Networks. © 2020 Murat Cancan, Iftikhar Ahmad, and Sarfarz Ahmad.
Nature of Graphs of Commutative Ring of Gaussian Integer Modulo N Under X3 - 1 Mapping
(Abdus Salam School of mathematical Sciences, 2021) Khalaf, A.J.M.; Nazeer, S.; Qayyum, K.; Cancan, M.
The aim of the present paper is to observe the structures of digraphs derived from the mappings f1: Zn[i] Zn[i] defined by f1 (x) = x3 — 1 whose vertex is Zn[i] = {a + bi: a, b (Formula presented) Zn} and for which there is a directed edge from x (Formula presented) Zn[i] to y (Formula presented) Zn[i] if and only if x3 — 1 = y (mod n). In this article, we investigated the structure of digraph. The in-degree of 1 and 0 in D1(n) are established where D1(n) is digraph obtained. Some regularity conditions of D1(n) are also discussed. For certain values of n, the simple conditions for the number of components and length of cycles is obtained. © 2021. All Rights Reserved.
On Asymptotically (Λ, Σ)-Statistical Equivalent Sequences of Fuzzy Numbers
(Springer, 2010) Savas, Ekrem; Sevli, H.; Cancan, M.
The goal of this paper is to give the asymptotically (lambda, sigma)-statistical equivalent which is a natural combination of the definition for asymptotically equivalent, invariant mean and lambda-statistical convergence of fuzzy numbers.