New Type Of Graph Research Articles

Valued-inverse dombi fuzzy graphs

Fuzzy graphs as labeled graphs (fuzzy vertex labeling and fuzzy edge labeling) have many applications in real life such as complex networks, coding theory, medical sciences, communication networks, and management sciences. Also, triangular norms as a special class of functions, have many applications in fuzzy set theory, probability and statistics, and other areas. This paper considers the notations of an inverse fuzzy graph and triangular norms to introduce the new type of graphs as valued-inverse Dombi fuzzy graphs. The valued-inverse Dombi fuzzy graphs are a generalization of inverse fuzzy graphs and are dual to Dombi fuzzy graphs. For any given greater than or equal to one real number, we construct a type of Dombi inverse fuzzy graph and investigate some conditions such that the product and union of Dombi inverse fuzzy graphs be a Dombi inverse fuzzy graph.

On graphs associated to topological spaces

Let 𝑋 be a set and (𝑋,𝑇) be a topological space. A new type of graph on 𝑃(𝑋), namely the closure graph of 𝑇 is introduced. The closure graph denoted by <em>Γ<sup>c</sup></em> whose vertex set is 𝑃(𝑋) in which two distinct vertices 𝐴 and 𝐵 are adjacent if <em>A</em>'∩<em>B</em>' ⊆ (<em>A</em>∩<em>B</em>)'. In this paper, the closure graph is shown as a simple, connected graph with diameter at most two. Furthermore, the girth of the closure graph <em>Γ<sup>c</sup></em>of 𝑇 is three if 𝑋 contains more than one point. Also, several graph properties are studied.

Descending endomorphism graphs of groups

We define a new type of graph of a group with reference to the descending endomorphisms of the group. A descending endomorphism of a group is an endomorphism that induces a corresponding endomorphism in every homomorphic image of the group. We define the undirected (directed) descending endomorphism graph of a group as the undirected (directed) graph whose vertex set is the underlying set of the group, in which there is an undirected (directed) edge from one vertex to another if the group has a descending endomorphism that maps the former element to the latter. We investigate some basic properties of these graphs and show that they are closely related to power graphs. We also determine the descending endomorphism graphs of symmetric, dihedral, and dicyclic groups.

Valued-inverse Dombi neutrosophic graph and application

<abstract><p>Utilizing two ideas of neutrosophic subsets (NS) and triangular norms, we introduce a new type of graph as valued-inverse Dombi neutrosophic graphs. The valued-inverse Dombi neutrosophic graphs are a generalization of inverse neutrosophic graphs and are dual to Dombi neutrosophic graphs. We present the concepts of (complete) strong valued-inverse Dombi neutrosophic graphs and analyze the complement of (complete) strong valued-inverse Dombi neutrosophic graphs and self-valued complemented valued-inverse Dombi neutrosophic graphs. Since the valued-inverse Dombi neutrosophic graphs depend on real values, solving the non-equation and the concept of homomorphism play a prominent role in determining the complete, strong, complementarity and self-complementarity of valued-inverse Dombi neutrosophic graphs. We introduce the truth membership order, indeterminacy membership order, falsity membership order, truth membership size, indeterminacy membership size and indeterminacy membership size of any given valued-inverse Dombi neutrosophic graph, which play a major role in the application of valued inverse Dombi neutrosophic graphs in complex networks. An application of a valued-inverse Dombi neutrosophic graph is also described in this study.</p></abstract>

Chain graph reduction into power chain graphs

Reduction of graphs is a class of procedures used to decrease the dimensionality of a given graph in which the properties of the reduced graph are to be induced from the properties of the larger original graph. This paper introduces both a new method for reducing chain graphs to simpler directed acyclic graphs (DAGs), that we call power chain graphs (PCG), as well as a procedure for structure learning of this new type of graph from correlational data of a Gaussian graphical model. A definition for PCGs is given, directly followed by the reduction method. The structure learning procedure is a two-step approach: first, the correlation matrix is used to cluster the variables; and then, the averaged correlation matrix is used to discover the DAGs using the PC-stable algorithm. The results of simulations are provided to illustrate the theoretical proposal, which demonstrate initial evidence for the validity of our procedure to recover the structure of power chain graphs. The paper ends with a discussion regarding suggestions for future studies as well as some practical implications.

On a generalized Cayley graph of column matrices of elements of a finite group

We introduce a new generalization of Cayley graphs. Moreover, we establish some basic properties of this new type of graph and we determine its structure under some assumptions.

Graph strongly by Qpre-closed set in topological spaces

In this paper, we summed a new type of graph called graph strongly Qpre-closed based on the functions resulting from cross-protected that use the sets. We did not show new types of relations, theorems, and illustrative examples about this new concept, which is considered one of the practical applications in the topological space and which is of great importance in our daily life.

On the spectra of generalized Fibonomial and Jacobsthal-binomial graphs

In this work, we first give a more general form of the binomial, Fibonomial, and balance-binomial graphs that is called generalized Fibonomial graph. We also argue the spectra of generalized Fibonomial graph. Next, we introduce a new type of graph on Jacobsthal numbers that is called Jacobsthal-binomial graph and denoted by $JB_{n}$. We obtain the adjacency, Laplacian and signless Laplacian characteristic polynomials of $JB_{n}$, respectively. We lastly give inequalities for the adjacency, Laplacian and signless Laplacian energies of $JB_{n}$.

A4-Graph of Finite Simple Groups


 Let G be a finite group and X be a conjugacy class of order 3 in G. In this paper, we introduce a new type of graphs, namely A4-graph of G, as a simple graph denoted by A4(G,X) which has X as a vertex set. Two vertices, x and y, are adjacent if and only if x≠y and x y-1=y x-1. General properties of the A4-graph as well as the structure of A4(G,X) when G@ 3D4(2) will be studied.

Computation of Vertex-Edge Degree Based Topological Descriptors for Hex-Derived Networks

A numeric number that represents the entire structure of a graph is defined to be a topological descriptor. Graph theory has been found to be a useful area of research in the direction of topological descriptors. The different physical and chemical properties of basic chemical compounds are related by main factors of topological descriptors. In the study of QSAR/QSPR, the vertex-edge topological descriptors are used to predict the bioactivity of chemical compound. The hex-derived networks are generated by hexagonal networks of dimension p, these networks have an assortment of valuable applications in computer science, medical science and engineering. Simonraj and George derived a new type of graphs, which is named a third type of hex-derived networks and this work carried out by Ali et al. with calculation of degree-based topological descriptors for these networks. In this paper, we compute the exact values of vertex-edge based topological descriptors for third type of hex-derived networks.

COVID-19 and the Restructuration of the International Trade in Century XXI

COVID-19 and the Restructuration of the International Trade in Century XXI

The Global Trade Closedness by COVID-19: The Case of EU

This paper presents a new methodology for studying trade closedness from a global pandemic such as COVID-19. The mission of this model is to offer policy-makers and researchers' a new analytical tool to study the impact of COVID-19 in world trade from a new perspective. We propose a new model entitled "The Global Trade Closedness Model (GTC-Model)," a simple and flexible model. The GTC-Model's general objective is to analyze the impact of a global pandemic on the imports in a specific period (in the short run). The study case is the European Union (EU) COVID-19 crisis from March to May 2020.The paper is divided into three parts. The first part is the literature reviews the literature on analytical methods evaluating openness based on three approaches focusing on political economy, economic theory, and trade policy. The second part will present a new analysis model to assess the trend, vulnerability, and harmonization of trade closedness. The relationship between trade closedness and COVID-19 infected cases growth is based on a new group of indicators and a new type of graph. The GTC-Model follows a series of steps in its application to study trade closedness growth and COVID-19 infected cases: (i) the degree of closedness by production sectors (Ci); (ii) closedness average rate (Ċ); (iii) harmonization of closedness (HC); (iv) average closedness growth rate (∆Ċ); (v) COVID-19 infected cases gross rate (∆COVID-19); (vi) closedness diamond graph; (vii) closedness/COVID-19 growth rate (∆Ċ: COVID-19) sensitivity analysis chart. The third part of this paper shows the results obtained from the application of GTC-Model in the European Union.

Inverse Fuzzy Graphs with Applications

Rosenfeld [A. Rosenfeld, Fuzzy Graphs, Fuzzy Sets and Their Applications, eds. L. A. Zadeh, K. S. Fu and M. Shimura (Academic Press, New York, 1975), pp. 77–95.] defined the fuzzy relations on the fuzzy sets and developed the structure of fuzzy graph, as a graph with a membership degree (between zero and one) for the vertices and edges such that the membership degree of every edge is less than or equal to the minimum of the membership degree of its endpoints. Although this model of graph has many applications in the real life, it fails to solve a lot of problems, which we can use graph for its representation. This paper aimed to demonstrate a new type of graph with a membership degree (between zero and one) for the vertices and edges so that the membership degree of every edge becomes more than or equals the minimum of the membership degrees of its endpoints. This new type of graph is called inverse fuzzy graph “or” I-fuzzy graph, which can play a role in solving many problems which are not solved by fuzzy graph.

Monotone Chromatic Number of Graphs

For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C: V (G) → {1, 2, ..., k} (using the non-negative integers {1, 2, ..., k} as colors). In this research work, we introduce a new type of graph coloring called monotone coloring, along with this new coloring, we define the monotone chromatic number of a graph and establish some related new graphs. Basic properties and exact values of the monotone chromatic number of some graph families, like standard graphs, Kragujevac trees and firefly graph are obtained. Also, we get a characterization for bipartite graphs by defining the monotone bipartite graph. Exact values of the monotone chromatic number for some special case of Cartesian product of graphs are found. Finally, upper and lower bounds for monotone chromatic number of the Cartesian product for non trivial connected graphs are presented.

New types of graphs induced by topological spaces

New types of graphs induced by topological spaces

Soft covering based rough graphs and corresponding decision making

Abstract Soft set theory and rough set theory are two new tools to discuss uncertainty. Graph theory is a nice way to depict certain information. Particularly soft graphs serve the purpose beautifully. In order to discuss uncertainty in soft graphs, some new types of graphs called soft covering based rough graphs are introduced. Several basic properties of these newly defined graphs are explored. Applications of soft covering based rough graphs in decision making can be very fruitful. In this regard an algorithm has been proposed.

Computing Degree Based Topological Properties of Third Type of Hex-Derived Networks

In chemical graph theory, a topological index is a numerical representation of a chemical network, while a topological descriptor correlates certain physicochemical characteristics of underlying chemical compounds besides its chemical representation. The graph plays a vital role in modeling and designing any chemical network. Simonraj et al. derived a new type of graphs, which is named a third type of hex-derived networks. In our work, we discuss the third type of hex-derived networks H D N 3 ( r ) , T H D N 3 ( r ) , R H D N 3 ( r ) , C H D N 3 ( r ) , and compute exact results for topological indices which are based on degrees of end vertices.

Uncertainty measurement for neighborhood based soft covering rough graphs with applications

Soft set theory and rough set theory are two newer tools to discuss uncertainty. Soft graphs are a nice way to depict certain information. In order to discuss uncertainty in soft graphs, a new type of graphs called neighborhood based soft covering rough graphs is introduced. We have discussed the uncertainty measures associated with neighborhood based soft covering rough graphs such as roughness measure, entropy measure and granularity. Some important properties of these uncertainty measures are investigated and the relationships between such measures are established. These properties will help to understand the essence of uncertainty measurement and in measuring the quality of a decision rule.

Bimagic Vertex Labelings

The notion of the equivalence of vertex labelings on a given graph is introduced. The equivalence of three bimagic labelings for regular graphs is proved. A particular solution is obtained for the problem of the existence of a 1-vertex bimagic vertex labeling of multipartite graphs, namely, for graphs isomorphic with Kn, n, m. It is proved that the sequence of bi-regular graphs Kn(ij) = ((Kn − 1 − M) + K1) − (unui) − (unuj) admits 1-vertex bimagic vertex labeling, where ui, uj is any pair of non-adjacent vertices in the graph Kn − 1 − M, un is a vertex of K1, M is perfect matching of the complete graph Kn − 1. It is established that if an r-regular graph G of order n is distance magic, then graph G + G has a 1-vertex bimagic vertex labeling with magic constants (n + 1)(n + r)/2 + n2 and (n + 1)(n + r)/2 + nr. Two new types of graphs that do not admit 1-vertex bimagic vertex labelings are defined.

Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators

In this work we have studied the Kleiss-Kuijf relations for the recently introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce quadratic Feynman propagators. By doing this, we were able to identify the non-planar one-loop Parke-Taylor factors. In order to check that, in fact, these new factors can describe non-planar amplitudes, we applied them to the bi-adjoint Φ3 theory. As a byproduct, we found a new type of graphs that we called the non-planar CHY-graphs. These graphs encode all the information for the subleading order at one-loop, and there is not an equivalent of these in the Feynman formalism.