Browsing by Author "Ediz, Suleyman"

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Base Polynomials for Degree and Distance Based Topological Invariants of N-Bilinear Straight Pentachain
(Taylor & Francis Ltd, 2021) Nizami, Abdul Rauf; Shabbir, Khurram; Sardar, Muhammad Shoaib; Qasim, Muhammad; Cancan, Murat; Ediz, Suleyman
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 difficult. Thus, we follow the divide and conquer rule and introduce the idea of base polynomials. We actually split the vertices into disjoint classes and then wrote the number of paths in terms of polynomials for each class, which ultimately serve as bases for Hosoya and Schultz polynomials. We also recover some indices from these polynomials. Finally, we give an example to show how these polynomials actually work.
Characteristic Sets Verses Generalized Characteristic Sets
(Taru Publications, 2021) Afzal, Farkhanda; Akram, Safia; Ashiq, Muhammad; Afzal, Deeba; Cancan, Murat; Ediz, Suleyman
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 into triangular form of a particular set/system. In this manuscript, a comparison of characteristic sets defined by Ritt-Wu's differential is provided with the generalized characteristic sets defined by author in [5]. Comparison shows that this scheme performs better than earlier method.
Degree-Based Entropy of Molecular Structure of Hac5c7[P,q]
(Sami Publishing Co-spc, 2021) Afzal, Farkhanda; Cancan, Murat; Ediz, Suleyman; Afzal, Deeba; Chaudhry, Faryal; Farahani, Mohammad Reza
This study aimed at 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 HAC(5)C(7)[p,q].
The Ediz Eccentric Connectivity Index of One Pentagonal Carbon Nanocones
(Taylor & Francis inc, 2013) Ediz, Suleyman
Let G be a molecular graph, the Ediz eccentric connectivity index is defined as (E)xi(c)(G) = Sigma(v is an element of V(G)) S-v/epsilon(v) where S-v is the sum of degrees of all vertices u, adjacent to vertex v, epsilon(v) is the largest distance between v and any other vertex u of G or the eccentricity of v. In this paper an exact formula for the Ediz eccentric connectivity index of one pentagonal carbon nanocones was computed.
Extremal Chemical Trees of the First Reverse Zagreb Beta Index
(Bulgarian Acad Science, 2018) Ediz, Suleyman; Semiz, Mesut
The reverse vertex degree of a vertex v of a simple connected graph G defined as c(v) = Delta - d(v) + 1, where Delta denotes the largest of all degrees of vertices of G and d(v) denotes the number of edges incident to v. The first reverse Zagreb beta index of a simple connected graph G defined as CM1 beta(G) = Sigma(uv is an element of E(G))(c(u) + c(v)). In this paper, we characterized maximum chemical trees with respect to the first reverse Zagreb beta index.
The First and Second Zagreb Polynomial and the Forgotten Polynomial of Cmxcn
(Sami Publishing Co-spc, 2020) Afzal, Farkhanda; Afzal, Deeba; Baig, Abdul Qudair; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
In this paper, the 1st and 2nd Zagreb polynomials and the forgotten polynomial of C(m)xC(n) were computed. Some degree-based topological indices such as 1st and 2nd multiple Zagreb indices, Hyper Zagreb index and the forgotten index or F-index of the given networks were also computed. In addition, we represented the outcome by graphical representation that describe the dependence of topological indices on the given parameters of polynomial structures.
Inverted Distance and Inverted Wiener Index
(Pushpa Publishing House, 2016) Ediz, Suleyman; Cancan, Murat
The Wiener index is the sum of distances between all pairs of vertices of a (connected) graph. In this paper, we define two novel graph invariants: the inverted distance and the inverted Wiener index. The inverted distance between any two different vertices u and v of a simple connected graph G is defined as: i(u, v) = D - d(u, v) + 1, where D denotes the diameter of G and d(u, v) denotes the distance of the vertices u and v. The inverted Wiener index of a simple connected graph G is defined as: IW(G) = Sigma(u not equal v) i(u, v), where the sum is taken over unordered pairs of vertices of G. We characterized maximum trees with respect to the inverted Wiener index.
Leap Indices and Their Polynomials of the Derived Graph of the Subdivision of Certain Polyphenyls
(Sami Publishing Co-spc, 2020) Asif, Fatima; Zahid, Zohaib; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
Topological indices are real (numerical) values which are associated with chemical compositions to correlate with chemical structure with different physical properties, chemical and biological activities. In this article, we computed and compared leap Zagreb indices and leap hyper-Zagreb indices of the derived graph of the subdivision of certain polyphenyls based on the 2-distance degree of the vertices.
M-Polynomial and Topological Indices Poly (Ethyleneamidoamine) Dendrimers
(Analytic Publ Co, 2020) Cancan, Murat; Ediz, Suleyman; Mutee-Ur-Rehman, Hafiz; Afzal, Deeba
Dendrimers are constructed by the successive addition of layers of branching groups. Topological indices are numerical numbers associated which are graph invariant up to isomorphism. In this report, we give closed form of M-polynomial of PETAA dendrimers and from this M-polynomial, we recover many topological indices. These topological indices help to predict physcio-chemical properties of the underling dendrimers, and help to the study of the properties of the materials of ship building. We also give graphical representation of our results.
Molecular Topological Properties of Alkylating Agents Based Anticancer Drug Candidates Via Some Ve-Degree Topological Indices
(Bentham Science Publ Ltd, 2020) Ediz, Suleyman; Cancan, Murat
Background: Reckoning molecular topological indices of drug structures gives the data about the underlying topology of these drug structures. Novel anticancer drugs have been leading by researchers to produce ideal drugs. Materials and Methods: Pharmacological properties of these new drug agents explored by utilizing simulation strategies. Topological indices additionally have been utilized to research pharmacological properties of some drug structures. Novel alkylating agents based anticancer drug candidates and ye-degree molecular topological indices have been introduced recently. Results and Conclusion: In this study we calculate ye-degree atom-bond connectivity, harmonic, geometric-arithmetic and sum-connectivity molecular topological indices for the newly defined alkylating agents based dual-target anticancer drug candidates.
More Topological Indices of Generalized Prism Network
(Analytic Publ Co, 2020) Cancan, Murat; Ediz, Suleyman; Fareed, Saba; Farahani, Mohammad Reza
Networks plays an important role in the field of engineering and topological indices can help us to get interesting properties if of underlined networks. With the help of topological indices, one can understand the topology and differentiate properties of different networks. The aim of this paper is to study the Generalized prism network which is very important for the researchers working in physics and engineering. We computed several degree-based indices, for example, sum connectivity index, Arithmetic-Geometric index, modified Randic, SK index, SK1 index, and SK2.
A Note on Angular Geometric Graphs
(Lebanese Univ, 2019) Ediz, Suleyman
In this short note we first define angular geometric graphs, angular degrees and geometric degrees in graph theory as follows. An angular geometric graph denoted as AGG is a graph in which given angles between vertices and edges can not be changed. If the angles are not given specifically in an angular geometric graph, all the angles are considered to be equal. The sum of the sines of the all angles of a vertex v is called the angular degree of v and denoted as ang(v). The sum of the degree of the vertex v and the angle degree of the vertex v is called the geometric degree of v and denoted as geom(v). The aim of this study is to investigate the geometric degrees of the Cartesian product of two paths and a path with a cycle.
A Note on Stratified Domination and 2-Rainbow Domination in Graphs
(Natl inst Optoelectronics, 2011) Aldemir, Mehmet Serif; Ediz, Suleyman
In this paper relations between stratified domination and 2-rainbow domination in graphs are investigated. And we conjectured that these two parameters are equal or 2-rainbow domination number is greater than stratified domination number by one.
On Computation of Latest Topological Descriptors of Some Cactus Chains Graphs Via M-Polynomial
(Taylor & Francis Ltd, 2021) Afzal, Farkhanda; Hussain, Hina; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
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-Banhatti, second K-Banhatti, first K-hyper Banhatti, second K-hyper Banhatti, modified first K-Banhatti, modified second K-Banhatti and harmonic K-Banhatti using their M-polynomials by the formulas given in [2]. Graphical analysis of the findings is also displayed. capability to recover the topological indices.
On Computation of M-Polynomial and Topological Indices of Starphene Graph
(Taru Publications, 2021) Chaudhry, Faryal; Ehsan, Muhammad; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Suleyman
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 different molecular structures supports us to calculate many topological indices. In this paper we calculate M-polynomial and topological indices for the starphene graph, then we recover numerous topological indices using the M-polynomials.
On Difference of Zagreb Indices
(Elsevier, 2014) Furtula, Boris; Gutman, Ivan; Ediz, Suleyman
The classical first and second Zagreb indices of a graph G are defined as M-1 = Sigma(v) d(v)(2) and M-2 = Sigma(uv) d(u) d(v), where d(v) is the degree of the vertex v of G. So far, the difference of M-1 and M-2 has not been studied. We show that this difference is closely related to the vertex-degree-based invariant RM2 = Sigma(uv) (d(u) - 1) (d(v) - 1), and determine a few basic properties of RM2. (C) 2014 Elsevier B.V. All rights reserved.
On K-Regular Edge Connectivity of Chemical Graphs
(de Gruyter Poland Sp Z O O, 2022) Ediz, Suleyman; Ciftci, Idris
Quantitative structure property research works, which are the essential part in chemical information and modelling, give basic underlying topological properties for chemical substances. This information enables conducting more feasible studies between theory and practice. Connectivity concept in chemical graph theory gives information about underlying topology of chemical structures, fault tolerance of molecules, and vulnerability of chemical networks. In this study we first defined two novel types of conditional connectivity measures based on regularity notion: k-regular edge connectivity and almost k-regular edge connectivity in chemical graph theory literature. We computed these new graph invariants for cycles, complete graphs, and Cartesian product of cycles. Our results will be applied to calculate k-regular edge connectivity of some nanotubes which are stated as Cartesian product of cycles. These calculations give information about fault tolerance capacity and vulnerability of these chemical structures.
On K-Total Distance Degrees and K-Total Wiener Polarity Index
(Taylor & Francis Ltd, 2021) Ediz, Suleyman; Ciftci, Idris; Cancan, Murat; Farahani, Mohammad Reza
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* (T), M-1 (T) and W-p(T) denotes 3-total Wiener polarity index, the first Zagreb index and Wiener polarity index, respectively for any tree T.
On Modified Eccentric Connectivity Index of Namn Nanotube
(Analytic Publ Co, 2020) Sajjad, Wasim; Sardar, Muhammad Shoaib; Cancan, Murat; Ediz, Suleyman; Baig, Abdul Qudair
Eccentricity based topological indices have attracted large attraction in the field of chemical graph theory. Eccentricity based topological indices are prominent due to their wide range applications. With the help of eccentricity based topological indices we can predict excellent accuracy rate in certain biological activities of diverse nature as com-pared to other indices. Carbon nanotubes are the cylindrical molecules that consist of rolled up sheets of carbon atoms. In this paper we consider the chemical graph of NA(m)(n) nanotube and compute an important eccentricity based topological index called Modified eccentric connectivity index.
On Novel Harmonic Indices of Certain Nanotubes
(Bioit internationaljournals, 2017) Ediz, Suleyman; Farahani, Mohammad Reza; Imran, Muhammad
Topological indices which are graph invariants derived from molecular graphs of molecules are used in QSPR researches for modeling physicochemical properties of molecules. Topological indices are important tools for determining the underlying topology of a molecule in view of theoretical chemistry. Most of the topological indices are defined by using classical degree concept of graph theory. In this study, we firstly define the new five versions of harmonic indices. And also we compute the fifth harmonic index of H-Naphtalenic nanotube and TUC4[m, n] nanotube.