# Murat CancanYuzuncu Yil University · Department of Mathematics

Murat Cancan

prof.

## About

143

Publications

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676

Citations

Citations since 2017

Introduction

Murat Cancan currently works at the Department of Mathematics Education, Yuzuncu Yil University. His main research areas are fixed point theory, graph theory and mathematics education.

## Publications

Publications (143)

Entropy is a measure of a system’s molecular disorder or unpredictability since work is produced by organized molecular motion. Shannon’s entropy metric is applied to represent a random graph’s variability. Entropy is a thermodynamic function in physics that, based on the variety of possible configurations for molecules to take, describes the rando...

Entropy is a thermodynamic function in physics that measures the randomness and disorder of molecules in a particular system or process based on the diversity of configurations that molecules might take. Distance-based entropy is used to address a wide range of problems in the domains of mathematics, biology, chemical graph theory, organic and inor...

Polyphenyls and their derivatives, which are used in heat exchangers, drug synthesis, organic synthesis, and so on, have attracted the attention of researchers in various fields for many years. In this paper, we determine the expected values of the augmented Zagreb and arithmetic-geometric indices for this class of conjugated hydrocarbons. The comp...

A topological index as a graph parameter was obtained mathematically from the graph’s topological structure. These indices are useful for measuring the various chemical characteristics of chemical compounds in the chemical graph theory. The number of atoms that surround an atom in the molecular structure of a chemical compound determines its valenc...

Entropy is essential. Entropy is a measure of a system’s molecular disorder or unpredictability, since work is produced by organized molecular motion. Entropy theory offers a profound understanding of the direction of spontaneous change for many commonplace events. A formal definition of a random graph exists. It deals with relational data’s probab...

The threat of developing a cancer therapy has been there for the past two to three decades. Almost 10 million people worldwide are affected by this illness each year. Anticancer medications are those that are used to treat cancer, a malignant condition. These anticancer medications come in a variety of types, such as hormones, antimetabolites, and...

Benzene is aromatic organic compound having six membered ring. Molecular studies provide evidence of presence of three alternative double bond providing exceptional stability to the molecule. Being basic unit of organic chemicals, benzene is widely used in pharmaceuticals, rubber, pesticides , dyes, lubricants, explosives and additives. Benzene der...

A topological index is a numerical parameter that is derived mathematically from a graph structure. In chemical graph theory, these indices are used to quantify the chemical properties of chemical compounds. We compute the first and second temperature, hyper temperature indices, the sum connectivity temperature index, the product connectivity tempe...

In this research paper, we prove that different families of comb graph are all cordial graphs.

In this research paper, we prove that different families of snake graphs such as triangular snake graph with pendant edges, alternate triangular snake graph with and without pendant edges, quadrilateral snake graph with and without pendant edges, alternate quadrilateral snake graph with pendant edges and double quadrilateral snake graph with and wi...

In this paper, discussion is made on the numerical solutions of ordinary differential equations of first order along with initial value problems by using Euler's Method, Modified Euler's Method and RK-4 Methods. Solutions and graphs of some numerical examples have been obtained with the help of MATLAB program as well as we determined the exact anal...

A topological index as a graph parameter is obtained mathematically from the graph's topological structure. These indices are useful in measuring the various chemical characteristics of chemical compounds in chemical graph theory. We compute the first and second temperature indices, the hyper temperature indices, the sum connectivity temperature in...

Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a variety of difficulties in biology, chemical graph theory, organic and inorganic chemistry, and othe...

Let [Formula: see text] be a simple, finite, undirected graph with [Formula: see text] vertices. The main purpose of this paper introduces the concepts of the minimum covering Gutman Estrada index, the minimum covering Seidel Estrada index, the minimum covering distance Estrada index, the minimum covering Randić Estrada index, the minimum covering...

Due to the epidemic that entered our lives in Turkey in 2020, face-to-face education activities have been moved to a different dimension through online and broadcast channels. The distance education approach is used to contribute to face-to-face education before the epidemic. However, due to the epidemic, distance education has been compulsory. Dur...

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. Hanan Ahmed et al. introduced novel topological indices known as domination topological indices. In this research work, we find...

Topological indices are extremely useful for analyzing various physical and chemical properties associated with a chemical compound. A topological index describes molecular structures by converting them into certain real numbers. Topological indices are used in the development of quantitative structure-activity relationships (QSARs) in which the bi...

Molecular descriptors explore the properties of graphs that endure constant after
recurrent changing in graph. These indices aid us to forecast chemical combinations like
entropy, enthalpy formation, area of surfaces and formation of heat. In structural chemistry para-line graphs are very popular. In this article, we present some valency based to...

In this paper, we determine the intuitionistic fuzzy stability of generalized additive functional equation by utilizing the fixed point technique.
https://www.philstat.org.ph/index.php/MSEA/issue/view/17

A chemical graph is a molecular complex that significantly explains the molecular structres. In this way atoms are identified by vertices and that are connected by lines known as edges of graph. Triangular benzenoids and starphene nanotubes are an inorganic compound with trigonal crystal system. We have computed the degree-based topological co-indi...

In graph coloring, labels are assigned to graph elements according to certain constraints. Colors are a special case of graph labeling. As well as 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, vert...

A variety of graphical invariants have been described and tested, offering lots of applications in the fields of nanochemistry, computational networks and in different scientific research areas. One commonly studied group of invariants is the topological index, which allows to research the chemical, biological, and physical properties of a chemical...

Abstract
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 fifteen edges. It is commonly used as a counter example to graph theory conjecture...

The topological index is a molecular predictor that is commonly supported in the research of QSAR of pharmaceuticals to numerically quantify their molecular features. Theoretical and statistical study of drug-like compounds improves the drug design and finding work-flow by rationalizing lead detection, instant decision, and mechanism of action comp...

The sum-connectivity index of a graph [Formula: see text] is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] in [Formula: see text], respectively. In this paper, w...

Sheehalli and Kanabur presented new forms of topological indices known as SK indices which have many applications in chemical graph theory towards QSPR/QSAR. A simple connected graph G is called a cactus graph if and only if any two cycles in the graph have no common edge. In this paper, we will explore and determine the sharp upper bounds of cactu...

Let F be the forgotten topological index of a graph G . The exponential of the forgotten topological index is defined as e F G = ∑ x , y ∈ S t x , y G e x 2 + y 2 , where t x , y G is the number of edges joining vertices of degree x and y . Let T n be the set of trees with n vertices; then, in this paper, we will show that the path P n has the mini...

Let [Formula: see text] be a graph with [Formula: see text] vertices and [Formula: see text] is the degree of its [Formula: see text]th vertex ([Formula: see text] is the degree of [Formula: see text]), then the Zagreb matrix of [Formula: see text] is the square matrix of order [Formula: see text] whose [Formula: see text]entry is equal to [Formula...

Abstract 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...

A topological index is invariant used to study the structure of molecular graph. In this paper we have generalized degree distance index, reciprocal degree distance index, Gutman index and reciprocal degree distance index and calculate generalized indices for splitting and co-splitting graphs.

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 goal of our research is to calculate degree-based connectivity Kulli-Basava indices of chemical graphs. These graphs include hammer-like-benzenoid and phenylene graphs. Several degree-based topological indices are calculated of hammer and phenylene graph.

The distance of a connected, simple graph ℙ is denoted by d(η1, η2), which is the length of a shortest path between the vertices η1, η2 ∈ V(ℙ), where V(ℙ) is the vertex set of ℙ. The l - ordered partition of V(ℙ) is θ = {θ1, θ2, … , θl}. A vertex η ∈ V(ℙ), and r(η|θ) = {d(η,θ1), d(η,θ2), … , d(η,θl)} be a l - tuple distances, where r(η|θ) is the re...

Power is considered as a boon for life, lifeline of a country's economy; a key instrument for the socio-economic evolution of any country. Pakistan faces the issue of power theft that worsens the economy of utilities. The purpose of research is to modernize Pakistan's power sector with the usage of Blockchain. Research is based on a comparative ana...

M-polynomial is introduced as a graph polynomial to re-cover closed formulas of degree based topological indices by using some suitable operators. These topological indices have a predicting ability about the properties of organic molecules. Silicate network (phyllosilicates) belonging to an important group of minerals that includes talc, micas, se...

The monotonic convergence of the a PD-type fractional-order iterative learning control algorithm is considered for a class of fractional-order linear systems. First, a theoretical analysis of the monotonic convergence of 1 st and 2 nd order a PD-type control algorithms is carried out in the typical terms of Lebesgue-p (L), p and the sufficient cond...

Chemical graph theory is a branch of mathematical chemistry which has an important outcome on the development of the chemical sciences. A chemical graph is a graph which is produced from some molecular structure by applying some graphical operations. The demonstration of chemical compounds and chemical networks with M-polynomials is a new idea and...

In this article, we recover many degree-based topological invariants using their formulas given in table [1] of Bismuth Tri-iodide by using its M-polynomial. The M-polynomial is a new phenomenon by which we can easily compute topological invariants of molecular graph. This is a very well-known fact that topological invariants play a key role in dec...

Coronavirus is able to cause illnesses ranging from the common flu to severe
respiratory disease. Today there is great competition among researchers and
physicians to cure COVID-19. Remdesivir is being studied for the COVID-19
treatment. In this article, we presented the topological analysis of remdesivir
with the help of M-polynomial. Proofs of th...

In this object, we present some new formulas of the reduced reciprocal Randić index, the arithmetic-geometric 1 index, the SK, SK1, SK2 indices, first Zagreb index, the general sum-connectivity index, the SCI index and the forgotten index. They were utilized for new degree-based topological indices via M-polynomial. We retrieved these topological i...

A topological index of graph G is a numerical quantity which describes its topology. If it is applied to molecular structure of a chemical compounds then it reflects the theoretical properties of the chemical compounds. In this article, well-known degree based topological indices are applied on chemical structures of medicine used for treatment of...

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...

The eccentricity-based entropy inspired by Shannon's entropy approach is the information-theoretic quantity to figure out the structural information of complex networks. The investigation for advance biomedical utilization of dendrimers has improved the synthesis of radical based molecules. Categorically, attaining radical dendrimers has initiated...

Topological coindices are topological indices that considers the non-contiguous sets of vertices. By utilizing graph basic investigation and deduction, we study the previously mentioned topological coindices of some synthetic atomic graphs that as often as possible show up in clinical, synthetic, and material designing, for example, Graphite Carbon...

Topological indices are numerical values that correlate the chemical structures with physical properties. In this article, we compute some reverse topological indices namely reverse Atom-bond connectivity index and reverse Geometric-arithmetic index for four different types of Benzenoid systems.

Porous materials, for example, metalnatural structures (MOFs) and their discrete partners metalnatural polyhedra (MOPs), that are built from coordinatively unsaturated inorganic hubs show incredible potential for application in gas adsorption/partition cycles, catalysis, and arising openings in hardware, optics, detecting, and biotechnology. A well...

Chemical graph theory is one of the dominant branches in graph theory. In this paper, we compute the atom bond connectivity, geometric arithmetic, first K-Banhatti, second K-Banhatti, first K-hyper Banhatti, second K-hyper Banhatti, modified first K-Banhatti, modified second K-Banhatti and harmonic K-Banhatti index via M-polynomial of zig-zag Benze...

The characteristics of various networks can be distinguished with the help of topological indices. The purpose of this paper is to study the generalized prism network, which is very interesting for physics and engineering researchers. For this network, we’re recovering some degree-based topological indices from the M-polynomial. We measure topologi...

The aim of this report is by using the calculated values of topological indices, degree weighted entropy of graph, the entropy measures are calculated viz., symmetric division index, inverse sum index atom-bond connectivity entropy and geometric arithmetic entropy for the nanotube HAC5C7[p,q].

In the field of chemical graph theory, topological indices are of great importance. The topological index is a numerical quantity dependent on different invariants or molecular graph characteristics. In the present article, the topological indices of para cacti chain graph are calculated such as atom bond connectivity, geometric arithmetic, first K...

This study investigates the relationship between classical degree and recently defined k-distance degree, ve-degree and ev-degree concepts in graph theory. We firstly define the k-total distance degree notion and investigate its relation with Zagreb and Wiener polarity indices. One of the main relation is W_3^* (T)=1/2 M_1 (T)+W_p (T) where W_3^* (...

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 t...

In this paper, we study the Von-Neumann regular elements of non-commutative rings M2(ℤ2) and M2(ℤ3). We prove that M2(ℤ2) and M3(ℤ3) are Von-Neumann rings. We also give code in C++to compute Von-Neumann regular elements of M2(ℤn).

Degree and distance-based graph polynomials are important not only as graph invariants but also for their applications in physics, chemistry, and pharmacy. The present paper is concerned with the Hosoya and Schultz polynomials of n-bilinear straight pentachain. It was observed that computing these polynomials directly by definitions is extremely di...

Nanomaterials are chemical compounds or substances which are moderately produced and used. Nanomaterials are engineered to reveal novel properties of nanocells that contrast with related non-visible substances, such as expanded consistency, conductivity or synthetic reaction. Topological indexes are quantities related to molecules that capture the...

In this paper, we discuss the degree based topological properties of the novel planar metal-organic networks TM – TCNB. Interestingly, the TM – TCNB systems are metallic in any event in one turn heading and show long-run ferromagnetic coupling on the off chance that for attractive structures, which speak to perfect applicants and a fascinating poss...

In this article we discuss the reverse degree based topological indices for planar metal-organic networks like transition metal (TM) of the three-dimensional series such as: Ti, V, Cr, :::, or Zn, phthalocyanine, and tetra-cyanobenzene (TCNB) as free-standing sheets. In distinction, the TM-TCNB networks are metallic at least in one revolutionary or...

Topological indices are numerical parameters used to study the physical and chemical residences of compounds. Degree-based topological indices have been studied extensively and can be correlated with many properties of the understudy compounds. In the factors of degree-based topological indices, M-polynomial played an important role. In this paper,...

Topological indices are important tools for QSPR researches. Wiener, Zagreb, and Randić indices are pioneers of topological indices as the most used topological indices in view of chemistry and chemical graph theory. These three topological indices have been used for modeling physical properties of octanes and other chemical molecules. We firstly d...

Corona virus cause diseases ranging from the common cold to Severe Acute Respiratory Syndrome (SARS). Several therapeutic agents have been evaluated for the treatment of Covid-19, but none have yet been shown to be efficacious. Remdesivir Gilead Sciences number (GS-5734), an inhibitor of the viral RNA-dependent, RNA polymerase with inhibitory activ...

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 ar...

The notion of characteristic sets that was developed by Ritt and Wu has been turned into an usual tool for study of set/systems of polynomial equations, algebraic as well as differential equations. By constructing a characteristic sets, one can triangularize an arbitrary set/system of any type of polynomials. It ensures that it can be decomposed in...

There is an incredible importance of topological indices in the field of graph theory. M-polynomial is a very effective way for finding the topological indices of a graph. In this article, some important topological indices such as Atom bond connectivity index, geometric-arithmetic index, K-Banhatti indices, Hyper K-Banhatti indices and Modified K-...

Chemical graph theory is a sub field of mathematical chemistry that is very beneficial in the progress of the computational analysis of the chemical compounds. A chemical graph is the outcome of the molecular structure by applying some graph The demonstration of chemical compounds with the M-polynomials is a developing idea and the M-polynomial of...

Nanomaterials are chemical compounds or substances which are moderately produced and used. Nanomaterials are engineered to reveal novel properties of nanocells that contrast with related non-visible substances, such as expanded consistency, conductivity or synthetic reaction. Topological indexes are quantities related to molecules that capture the...