Ismail naci Cangul

Bursa Uludag University

This paper aims to analyze the decision-making processes in which the interactions between objects belonging to two different universe sets are desired to be determined. In this direction, first of all, the concepts of object interaction and inverse object interaction sets for two different universe sets are defined. In addition, considering binary...

This research paper focuses on the computation and analysis of molecular descriptors or topological indices for a generalised Kneser-type bi-partite graph called bipartite Kneser B type-k graph denoted by H B (n, k). Topological indices are formulae that are obtained from graph connectivity patterns and are used to summarise and compress the data t...

Background Let G be a connected graph and S be a k element subset of the vertex set V(G) of G. Steiner distance is a natural generalization of the usual graph distance. The Steiner-k distance dG(S) between the vertices of S is the minimum size among all connected subgraphs whose vertex set contains S. The generalized indices based on Steiner distan...

The purpose of this paper is to introduce and investigate the atom bond-connectivity energy ABCE(G) of a graph G. We present some upper and lower bounds for ABCE(G) and calculate it for several graph classes and also for some graphs with one edge deleted which enables us to calculate this index for larger graphs by means of smaller graphs. Also ABC...

Background In graph theory, M polynomials like the matching polynomial are very crucial in examining the matching structures within graphs, while NM polynomials extends this to analyze non-matching edges. These polynomials are important in many fields, including chemistry and network architecture. They support the derivation of topological indices...

Let G be a finite order graph. Its resolvent matrix and its resolvent energy are respectively given by R ξ (A(G)) = (A(G)-ξI)-1 and ER(G) = Σ n i = 1 (n-λ i)-1. For some classes of weighted graphs, we know that λ 1 = n which means that the formula for ER(G) is not applicable. In this work, the pseudo-resolvent energy for those classes of graphs are...

Let $\mathscr{B}_n = \{ \pm x_1, \pm x_2, \pm x_3, \cdots, \pm x_{n-1}, x_n \}$ where $n>1$ is fixed, $x_i \in \mathbb{R}^+$, $i = 1, 2, 3, \cdots, n$ and $x_1 < x_2 < x_3 < \cdots < x_n$. Let $\phi(\mathscr{B}_n)$ be the set of all non-empty subsets $S = \{u_1, u_2,\cdots, u_t\}$ of $\mathscr{B}_n$ such that $|u_1|<|u_2|<\cdots <|u_{t-1}|<u_t $ wh...

This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation pro...

Graph theory received a great attention in chemical graph theory which is a branch of mathematical chemistry to model a molecule through a graph where vertices are considered as the atoms of the molecule and edges are considered as the bonds between them. A topological index or molecular descriptor of a graph is a numeric quantity obtained mathemat...

Background: The degree sequence of a graph is the list of its vertex degrees arranged in usually increasing order. Many properties of the graphs realized from a degree sequence can be deduced by means of a recently introduced graph invariant called omega invariant. Methods: We used the definitions of the considered graph products together with the...

Nanomaterials have been widely used in a number of sectors during the past few decades, including electronics, pharmaceuticals , cosmetics, food processing, construction, and aeronautics. These nanomaterials may improve approaches for therapy, diagnosis, and prevention in the medical field. Graphene oxide (GO), an oxidised derivative of graphene, i...

The sum-connectivity variant of atom-bond connectivity index is recently introduced, and is defined as the sum of the terms of the form $\sqrt{(d_u+d_v-2)/(d_u+d_v)}$ over all adjacent vertices $u, v$ in a graph $G$, and named as the atom-bond sum connectivity index denoted by $ABS(G)$. The sum of the absolute values of all the eigenvalues of the a...

M polynomials and NM polynomials are integral concepts in polynomial graph theory. M polynomials, like the matching polynomial, provide insights into matching structures in graphs, while NM polynomials extend this to non-matching edges. These tools are crucial in understanding graph properties and are applied in diverse fields such as network desig...

Molecular and spectral graph theory deals with modeling the molecular structure by a graph and to obtain some numerical value by studying this graph by mathematical methods to comment on physico-chemical properties of the molecular structure under investigation. One of the main tools to do this is Topological graph indices. There are thousands of d...

A vertex degree based topological index called the Sombor index was recently defined in 2021 by Gutman and has been very popular amongst chemists and mathematicians. We determine the amount of change of the Sombor index when some elements are removed from a graph. This is done for several graph elements, including a vertex, an edge, a cut vertex, a...

In this work, we consider four families of nanotubes and computed the sum connectivity delta Banhatti and product connectivity delta Banhatti indices and the corresponding exponentials of their graphs. Furthermore, by using vertex and edge partitions of these graphs we computed these connectivity delta Banhatti indices and their corresponding expon...

Let G = (V, E) be a simple graph with n vertices and m edges. ν(G) and c(G) = m − n + θ be the matching number and cyclomatic number of G, where θ is the number of connected components of G, respectively. Wang and Wong in [18] provided formulae for the upper and the lower bounds of the nullity η(G) of G as η(G) = n − 2ν(G) + 2c(G) and η(G) = n − 2ν...

Sombor index was recently defined in 2021 as a new vertex degree based topological index by Gutman and has received great attention of mathematicians and chemists. In this work, we determine how much the Sombor index is effected when we delete a vertex or an edge from a graph. Using the formulae obtained here successively, one can calculate the Som...

Background The omega index has been recently introduced to identify a variety of topological and combinatorial aspects of a graph with a new viewpoint. As a continuing study of the omega index, by considering the incidence of edges and vertices to the adjacency of the vertices, in this paper, we have introduced the second omega index Ω2 and then co...

This is an Open Access Journal / article distributed under the terms of the Creative Commons Attribution License (CC BY-NC-ND 3.0) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. All rights reserved. The aim of this short paper is to carry a QSPR analysis for physical prope...

In this short paper, a QSPR analysis is carried for first stress index of molecular graphs and physical properties of lower alkanes and linear regression models are presented for boiling points, molar volumes, molar refractions, heats of vaporization, critical temperatures, critical pressures and surface tensions.

In Chemical Graph Theory, several degree based topological indices were introduced and studied since 1947. Some of these have important applications in chemistry while some only have nice mathematical properties. In this paper, we introduce the Nirmala leap index and modified Nirmala leap index, their polynomials and compute these indices for some...

The Randić \(\mathcal {R}(G)\) of a graph G is one of the classical graph-based molecular descriptors that found countless applications in chemistry, pharmacology, electronical engineering, networks, etc. The mathematical properties of Randić index are also well elaborated. The Randić index of an organic molecule whose molecular graph is G which is...

In the recent decades, many degree-based energies are introduced in Discrete Mathematics. The current paper is dealing with the study of general Randić energy, sum-connectivity energy, SDD energy and degree square sum energy of m-splitting and m-shadow graphs.KeywordsRandić energySDD energym-splitting graphsm-shadow graphsAMS 2010 Subject Classific...

The single valued neutrosophic probabilistic hesitant fuzzy rough Einstein aggregation operator (SV-NPHFRE-AO) is an extension of the neutrosophic probabilistic hesitant fuzzy rough set theory. It is a powerful decision-making tool that combines the concepts of neutrosophic logic, probability theory, hesitant fuzzy sets, rough sets, and Einstein ag...

A total k-labeling is a function fe from the edge set to the set {1, 2, . . . , ke} and a function fv from the vertex set to the set {0, 2, 4, . . . , 2kv}, where k = max{ke, 2kv}. A distance irregular reflexive k-labeling of the graph G is the total k-labeling, if for every two different vertices u and u 0 of G, w(u) 6= w(u 0 ), where w(u) = Σui∈N...

Chemical graph theory is currently expanding the use of topological indices to numerically encode chemical structure. The prediction of the characteristics provided by the chemical structure of the molecule is a key feature of these topological indices. The concepts from graph theory are presented in a brief discussion of one of its many applicatio...

The ABC index is one of the most applicable topological graph indices and several properties of it has been studied already due to its extensive chemical applications. Several variants of it have also been de�fined and used for several reasons. In this paper, we calculate the atom-bond connectivity index of some derived graphs such as double graphs...

To deal with the uncertainty and ensure the sustainability of the manufacturing industry, we designed a multi criteria decision-making technique based on a list of unique operators for single-valued neutrosophic hesitant fuzzy rough (SV-NHFR) environments with a high confidence level. We show that, in contrast to the neutrosophic rough average and...

Randić index is one of the most famous topological graph indices. The energy of a graph was defined more than four decades ago for its molecular applications. The classical energy of a graph modeling a molecule is defined as the sum of absolute values of all the eigenvalues of the adjacency matrix corresponding to the modeling graph. There are seve...

We developed a multicriteria decision-making method based on the list of novel single-valued neutrosophic hesitant fuzzy rough (SV-NHFR) weighted averaging and geometric aggregation operators to address the uncertainty and achieve the sustainability of the manufacturing business. In addition, a case study on choosing the optimum elements for a sust...

In graph theory, lattices are used when some structural part of the graph repeats itself finitely or infinitely many times. They have applications in complex analysis and geometry in mathematics, and also natural applications in chemical graph theory. As a lattice can be taken as a graph, it is also possible to use them in the study of large networ...

In this paper, we obtain some upper and lower bounds for the spectral radius of some special matrices such as maximum degree, minimum degree, Randic, sum-connectivity, degree sum, degree square sum, first Zagreb and second Zagreb matrices of a simple connected graph G by the help of matrix theory. We also get some upper bounds for the corresponding...

In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced reciprocal Randic index, Narumi-Katayama index and symmetric division index a graph using solely the vertex degrees. Then we obtain upper and lower bounds for these indices for the complete graphs, path graphs and Fibonacci-sum graphs. Finally, we compar...

Establishing new relationships between the physical properties and the molecular structure of chemical compounds is very exciting. In this short paper, a QSPR analysis is carried for physical properties of lower alkanes involving Peripheral Wiener index, number of paths of length 3 and the number of vertices in molecular graphs and best multiple li...

A total k-labeling is defined as a function g from the edge set to the first natural number ke and a function f from the vertex set to a non-negative even number up to 2kv, where k = max{ke, 2kv}. A vertex irregular reflexive k-labeling of the graph G is total k-labeling if wt(x) ¹ wt(x¢) for every two different vertices x and x¢ of G, where wt(x)...

e molecular topology of a graph is described by topological indices, which are numerical measures. In theoretical chemistry, topological indices are numerical quantities that are used to represent the molecular topology of networks. ese topological indices can be used to calculate several physical and chemical properties of chemical compounds, such...

Polysaccharides are biomaterial with great biocompatibility, biodegradability, and low toxicity. ere are long chains of monosaccharide units linked together by glycosidic bonds. ey have a wide spectrum of functional properties and are essential to life's survival. ese are a makeup of storage polysaccharides (such as starch and glycogen). Starch is...

Polysaccharides are biomaterial with great biocompatibility, biodegradability, and low toxicity. There are long chains of monosaccharide units linked together by glycosidic bonds. They have a wide spectrum of functional properties and are essential to life’s survival. These are a makeup of storage polysaccharides (such as starch and glycogen). Star...

Recently, some topological graph indices of pentagonal chains and pentagonal double chains are studied and here, we study some topological graph indices of pentagonal triple chains similarly to these previous works. We make use of the vertex and edge partitions of these graphs and calculate their indices by means of these partitions and combinatori...

There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, w...

In this paper, we present the concept of \(\alpha \)-split domination in graphs. Besides, we calculate the \(\alpha \)-split domination number of path, cycle, complete bipartite graphs and discuss the upper bounds for \(\alpha \)-split domination number in terms of order p, size q and the maximum degree \(\varDelta \). We prove that \(\alpha \)-spl...

In this paper, the determinant of the sum-edge adjacency matrix of any given graph without loops is calculated by means of an algebraic method using spanning elementary subgraphs and also the coefficients of the corresponding sum-edge characteristic polynomial are determined by means of the elementary subgraphs. Also we gave a formula for the numbe...

Energy of a graph, firstly defined by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix, in other words the sum of absolute values of the roots of the characteristic (spectral) polynomials, is an important sub area of graph theory. Symmetry and regularity are two important and desired properties in many areas includ...

In this paper we establish new inequalities involving Randi$\acute{c}$ index, weigthed Randi$\acute{c}$ index and general Randi$\acute{c}$ index in terms of the eigenvalues, the number of edges, the number of vertices, the energy and vertex degrees.

with abstract

Let vi and vj be two vertices of a graph G. The maximum degree matrix of G is given in [2] by dij = max {di, dj} if vi and vj are adjacent 0 otherwise. Similarly the (i, j)-th entry of the minimum degree matrix is defined by taking the minimum degree instead of the maximum degree above, [1]. In this paper, we have elucidated a relation between maxi...

In this paper, we introduce the Merrifield-Simmons vector defined at a path of corresponding double hexagonal (benzenoid) chain. By utilizing this vector, we present reduction formulae to compute the Merrifield-Simmons index σ(H) of the corresponding double hexagonal (benzenoid) chain H. As the result, we compute σ(H) of H by means of a product of...

In this paper, the concept of accessibility integrity is introduced as a new measure of the stability of a graph $G$ and it is defined as $$AI(G)=\min\{|S|+m(G-S)\},$$ where $S$ is an accessible set and $m(G-S)$ is the order of a maximum component of $G-S$. First, the accessibility integrity of some graphs is obtained and the relations between acce...

Average degree of a graph is defined to be a graph invariant equal to the arithmetic mean of all vertex degrees and has many applications, especially in determining the irregularity degrees of networks and social sciences. In this study, some properties of average degree have been studied. Effect of vertex deletion on this degree has been determine...

Topological graph indices have been of great interest in the research of several properties of chemical substances as it is possible to obtain these properties only by using mathematical calculations. The irregularity indices are the ones to determine the degree of irregularity of a graph. Albertson and Bell indices are two of them. Edge and vertex...

For the vertex set V G of a graph G , the sum of reciprocals of the breadth (distances) between the vertex v ∈ V G and whole other remaining vertices of G is called reciprocal status of v . In this study, first of all, we introduced the V L reciprocal status index and V L reciprocal status co-index of a graph G . Later, we exposed some sharp bounds...

Gutman et al. gave some relations for computing the Hosoya indices of two special benzenoid systems R_n and P_n. In this paper, we compute the Hosoya index and Merrifield-Simmons index of R_n and P_n by means of introducing four vectors for each benzenoid system and index. As a result, we compute the Hosoya index and the Merrifield-Simmons index of...

A derived graph is a graph obtained from a given graph according to some predetermined rules. Two of the most frequently used derived graphs are the line graph and the total graph. Calculating some properties of a derived graph helps to calculate the same properties of the original graph. For this reason, the relations between a graph and its deriv...

An [Formula: see text]-dynamic coloring of a graph [Formula: see text] is a proper coloring [Formula: see text] of the vertices such that [Formula: see text] for each vertex [Formula: see text]. The [Formula: see text]-dynamic chromatic number of a graph [Formula: see text] is the minimum [Formula: see text] such that [Formula: see text] has an [Fo...

Molecules can be modelled by graphs to obtain their required properties by means of only mathematical methods and formulae. In this paper, several degree-based graph indices of one of the important chemical compounds called as polyester are calculated to determine several chemical and physicochemical properties of polyester.

In many areas of science, lattice structures are very useful phenomenons. In network sciences, in chemistry and in social sciences, we face them in the solution of many daily life problems. Several large lattice structures can also be thought as graphs and in that way, are useful in the study of large networks. A very recently defined and studied c...

The stress of a vertex in a graph had been introduced by Shimbel in 1953 as the number of geodesics (shortest paths) passing through it. A topological index of a chemical structure (molecular graph) is a number that correlates given chemical structure with a chemical reactivity or physical property. In this paper, we introduce two new topological i...

An Lh,k-labeling of a graph G=V,E is a function f:V⟶0,∞ such that the positive difference between labels of the neighbouring vertices is at least h and the positive difference between the vertices separated by a distance 2 is at least k. The difference between the highest and lowest assigned values is the index of an Lh,k-labeling. The minimum numb...

A set S ⊆ V of a graph G = V , E is called a co-independent liar’s dominating set of G if (i) for all v ∈ V , N G v ∩ S ≥ 2 , (ii) for every pair u , v ∈ V of distinct vertices, N G u ∪ N G v ∩ S ≥ 3 , and (iii) the induced subgraph of G on V − S has no edge. The minimum cardinality of vertices in such a set is called the co-independent liar’s domi...

In this study, we examine some graph parameters such as the edgenumber, chromatic number, girth, domination number and cliquenumber of power set graphs

Let $G$ be a graph with $n$ vertices and let $d_i$ denote the degree of the vertex $v_i$. For a given graph, there are more than 100 matrices obtained by using some properties of the graph. Most important and used ones are the adjacency, incidency and Laplacian matrices. Recently, several graph topological indices have been used in defining new gra...

The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO=SO(G)=∑vivj∈E(G)dG(vi)2+dG(vj)2, where dG(vi) is the degree of vertex vi in G. Here, we present novel lower and upper bounds on the Sombor index of graphs by using some...

Algebraic study of graphs is a relatively recent subject which arose in two main streams: One is named as the spectral graph theory and the second one deals with graphs over several algebraic structures. Topological graph indices are widely-used tools in especially molecular graph theory and mathematical chemistry due to their time and money saving...

Graph theory is one of the rising areas in mathematics due to its applications in many areas of science. Amongst several study areas in graph theory, spectral graph theory and topological descriptors are in front rows. These descriptors are widely used in QSPR/QSAR studies in mathematical chemistry. Vertex-semitotal graphs are one of the derived gr...

The transmission of a vertex u in a connected graph G is defined as the sum of thedistances between u and all other vertices of a graph G. The reciprocal transmission of a vertex u in a connected graph G is defined as the sum of the reciprocal of distances between u and all other vertices of a graph G. In this paper, we introduce and study new topo...

In this paper, we calculate the Randić type hadi index of some standard graphs, double graphs, subdivision graphs, complements and line graphs. Also we compute the index for the chemical structure graphene.

The eccentric-connectivity index of a graph G is the sum of the products of the eccentricity and the degree of each vertex in G. In this paper, we define four new invariants related to the eccentric-connectivity index and obtain upper bounds for total transformation graphs which are some generalizations of total graph.

Apart from its applications in Chemistry, Biology, Physics, Social Sciences, Anthropology, etc., there are close relations between graph theory and other areas of Mathematics. Fibonacci numbers are of utmost interest due to their relation with the golden ratio and also