Vague Graphs Research Articles

A Novel Domination in Vague Influence Graphs with an Application

Vague influence graphs (VIGs) are well articulated, useful and practical tools for managing the uncertainty preoccupied in all real-life difficulties where ambiguous facts, figures and explorations are explained. A VIG gives the information about the effect of a vertex on the edge. In this paper, we present the domination concept for VIG. Some issues and results of the domination in vague graphs (VGs) are also developed in VIGs. We defined some basic notions in the VIGs such as the walk, path, strength of In-pair , strong In-pair, In-cut vertex, In-cut pair (CP), complete VIG and strong pair domination number in VIG. Finally, an application of domination in illegal drug trade was introduced.

A Study on Regular Domination in Vague Graphs with Application

Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In graph theory, a dominating set (DS) for a graph G ∗ = X , E is a subset S of the vertices X such that every vertex not in S is adjacent to at least one member of S . The concept of DS in FGs has received the attention of many researchers due to its many applications in various fields such as computer science and electronic networks. In this paper, we introduce the notion of ϵ 1 , ϵ 2 , 2 -Regular vague dominating set and provide some examples to explain various concepts introduced. Also, some results were discussed. Additionally, the ϵ 1 , ϵ 2 , 2 -Regular strong (weak) and independent strong (weak) domination sets for vague domination set (VDS) were presented with some theorems to support the context.

Some Properties of Double Domination in Vague Graphs with an Application

This paper is devoted to the study of the double domination in vague graphs, and it is a contribution to the Special Issue “Advances in graph theory and Symmetry/Asymmetry” of Symmetry. Symmetry is one of the most important criteria that illustrate the structure and properties of fuzzy graphs. It has many applications in dominating sets and helps find a suitable place for construction. Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In the graph theory, a dominating set (DS) for a graph G*=(X,E) is a subset D of the vertices X so that every vertex which is not in D is adjacent to at least one member of D. The subject of energy in graph theory is one of the most attractive topics serving a very important role in biological and chemical sciences. Hence, in this work, we express the notion of energy on a dominating vague graph (DVG) and also use the concept of energy in modeling problems related to DVGs. Moreover, we introduce a new notion of a double dominating vague graph (DDVG) and provide some examples to explain various concepts introduced. Finally, we present an application of energy on DVGs.

New concepts on level graphs of vague graphs with application in medicine

Vague graphs (VGs), belonging to the fuzzy graph (FG) family, have good capabilities when facing problems that cannot be expressed by FGs. When an element membership is unclear, neutrality is a good option that can be well-supported by a VG. The previous definitions limitations in FG have led us to offer new definitions in VGs. Therefore, this study introduces the notion of vague edge graph (VEG) ζ̂=(V,N), in which V is a crisp vertex set and N is a vague relation (VR) on M, presenting some of its properties. Using λ-level graphs (LGs) and (λ, δ)-LGs, we characterize VG ζ = (M, N), where M is a vague set (VS) on V and N is a VR on V. Medical diagnosis is one of the most sensitive and important issues in the medical sciences. If it is not done properly, the patient will suffer irreparable damage. Therefore, an application of VG in the diagnosis of the disease is expressed.

New concepts of product vague graphs with applications

New concepts of product vague graphs with applications

New concepts of product vague graphs with applications

New concepts of product vague graphs with applications

Energy of Vague Fuzzy Graph Structure and Its Application in Decision Making

Vague graphs (VGs), belonging to the fuzzy graphs (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. The notion of a VG is a new mathematical attitude to model the ambiguity and uncertainty in decision-making issues. A vague fuzzy graph structure (VFGS) is the generalization of the VG. It is a powerful and useful tool to find the influential person in various relations. VFGSs can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problems where fuzzy graphs may fail to reveal satisfactory results. Moreover, VGSs are very useful tools for the study of different domains of computer science such as networking, social systems, and other issues such as bioscience and medical science. The subject of energy in graph theory is one of the most attractive topics that is very important in biological and chemical sciences. Hence, in this work, we extend the notion of energy of a VG to the energy of a VFGS and also use the concept of energy in modeling problems related to VFGS. Actually, our purpose is to develop a notion of VFGS and investigate energy and Laplacian energy (LE) on this graph. We define the adjacency matrix (AM) concept, energy, and LE of a VFGS. Finally, we present three applications of the energy in decision-making problems.

Connectivity Index in Vague Graphs with Application in Construction

The vague graph (VG), which has recently gained a place in the family of fuzzy graph (FG), has shown good capabilities in the face of problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. Connectivity index (CI) in graphs is a fundamental issue in fuzzy graph theory that has wide applications in the real world. The previous definitions’ limitations in the connectivity of fuzzy graphs directed us to offer new classifications in vague graph. Hence, in this paper, we investigate connectivity index, average connectivity index, and Randic index in vague graphs with several examples. Also, one of the motives of this research is to introduce some special types of vertices such as vague connectivity enhancing vertex, vague connectivity reducing vertex, and vague connectivity neutral vertex with their properties. Finally, an application of connectivity index in the selected town for building hospital is presented.

Novel Concepts in Vague Graphs with Application in Hospital’s Management System

Many problems of practical interest can be modeled and solved by using vague graph (VG) algorithms. Vague graphs, belonging to the fuzzy graphs (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. Hence, in this paper, we introduce the notion of (η, γ)‐ HMs of VGs and classify homomorphisms (HMs), weak isomorphisms (WIs), and coweak isomorphisms (CWIs) of VGs by (η, γ)‐ HMs. Hospitals are very important organizations whose existence is directly related to the general health of the community. Hence, since the management in each ward of the hospital is very important, we have tried to determine the most effective person in a hospital based on the performance of its staff.

Certain Concepts in Vague Graph with an Application

Vague graphs (VGs), belonging to the FGs family, have good capabilities when faced with problems that cannot be expressed by FGs. When an element’s membership is not clear, neutrality is a good option that can be well‐supported by a VG. The previous definition limitations in irregular‐FG have led us to offer new definitions in VGs. So, in this paper, we introduce the concepts of strongly edged irregular vague graphs (SEIVGs), strongly edged totally irregular vague graphs (SETIVGs), and perfectly regular vague graphs (PRVGs) with several examples. A comparative study between SEIVGs and SETIVGs is presented. Finally, an application of vague influence digraph has been presented.

A Novel Description on Vague Graph with Application in Transportation Systems

Fuzzy graph (FG) models embrace the ubiquity of existing in natural and man-made structures, specifically dynamic processes in physical, biological, and social systems. It is exceedingly difficult for an expert to model those problems based on a FG because of the inconsistent and indeterminate information inherent in real-life problems being often uncertain. Vague graph (VG) can deal with the uncertainty associated with the inconsistent and determinate information of any real-world problem, where FGs many fail to reveal satisfactory results. Regularity definitions have been of high significance in the network heterogeneity study, which have implications in networks found across biology, ecology, and economy; so, adjacency sequence (AS) and fundamental sequences (FS) of regular vague graphs (RVGs) are defined with examples. One essential and adequate prerequisite has been ascribed to a VG with maximum four vertices is that it should be regular based on the adjacency sequences concept. Likewise, it is described that if ζ and its principal crisp graph (CG) are regular, then all the nodes do not have to have the similar AS. In the following, we obtain a characterization of vague detour (VD) g-eccentric node, and the concepts of vague detour g-boundary nodes and vague detour g-interior nodes in a VG are examined. Finally, an application of vague detour g-distance in transportation systems is given.

2-Domination in vague graphs

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, the notions of (perfect-total) 2-dominating set and (perfect-total) 2-domination numbers on vague graphs are introduced and some properties are investigated. Especially, it is proven that in any strong vague graph on a Petersen graph, any minimal 2-dominating set is a minimal perfect 2-dominating set and minimal dominating set. Then, the concepts of (total) 2-cobondage set and (total) 2-cobondage number in vague graphs are expressed and related results obtained. Finally, an application related to Fire Stations and Emergency Medical centers is provided.

Certain Properties of Domination in Product Vague Graphs With an Application in Medicine

The product vague graph (PVG) is one of the most significant issues in fuzzy graph theory, which has many applications in the medical sciences today. The PVG can manage the uncertainty, connected to the unpredictable and unspecified data of all real-world problems, in which fuzzy graphs (FGs) will not conceivably ensue into generating adequate results. The limitations of previous definitions in FGs have led us to present new definitions in PVGs. Domination is one of the highly remarkable areas in fuzzy graph theory that have many applications in medical and computer sciences. Therefore, in this study, we introduce distinctive concepts and properties related to domination in product vague graphs such as the edge dominating set, total dominating set, perfect dominating set, global dominating set, and edge independent set, with some examples. Finally, we propose an implementation of the concept of a dominating set in medicine that is related to the COVID-19 pandemic.

Novel Concepts of Domination in Vague Graphs with Application in Medicine

VG can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which FGs possibly will not succeed in bringing about satisfactory results. The previous definitions’ restrictions in FGs have made us present new definitions in VGs. A wide range of applications have been attributed to the domination in graph theory for several fields such as facility location problem, school bus routing, modeling biological networks, and coding theory. Therefore, in this research, we study several concepts of domination, such as restrained dominating set (RDS), perfect dominating set (PDS), global restrained dominating set (GRDS), total k -dominating set, and equitable dominating set (EDS) in VGs and also introduce their properties by some examples. Finally, we try to represent the application and importance of domination in the field of medical science and discuss the topic in today’s world, namely, the corona vaccine.

A Survey on Domination in Vague Graphs with Application in Transferring Cancer Patients between Countries

Many problems of practical interest can be modeled and solved by using fuzzy graph (FG) algorithms. In general, fuzzy graph theory has a wide range of application in various fields. Since indeterminate information is an essential real-life problem and is often uncertain, modeling these problems based on FG is highly demanding for an expert. A vague graph (VG) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems in which fuzzy graphs may not succeed in bringing about satisfactory results. Domination in FGs theory is one of the most widely used concepts in various sciences, including psychology, computer sciences, nervous systems, artificial intelligence, decision-making theory, etc. Many research studies today are trying to find other applications for domination in their field of interest. Hence, in this paper, we introduce different kinds of domination sets, such as the edge dominating set (EDS), the total edge dominating set (TEDS), the global dominating set (GDS), and the restrained dominating set (RDS), in product vague graphs (PVGs) and try to represent the properties of each by giving some examples. The relation between independent edge sets (IESs) and edge covering sets (ECSs) are established. Moreover, we derive the necessary and sufficient conditions for an edge dominating set to be minimal and show when a dominance set can be a global dominance set. Finally, we try to explain the relationship between a restrained dominating set and a restrained independent set with an example. Today, we see that there are still diseases that can only be treated in certain countries because they require a long treatment period with special medical devices. One of these diseases is leukemia, which severely affects the immune system and the body’s defenses, making it impossible for the patient to continue living a normal life. Therefore, in this paper, using a dominating set, we try to categorize countries that are in a more favorable position in terms of medical facilities, so that we can transfer the patients to a suitable hospital in the countries better suited in terms of both cost and distance.

Irregular vague graphs

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, the new concepts of (totally) irregular, strongly (totally) irregular, highly totally irregular, neighborly totally irregular, edge-irregular of vague graphs are introduced and generalized, and some properties and related results are investigated. Then, we present the concepts of homomorphism, weak isomorphism, co-weak isomorphism and isomorphism of irregular vague graphs and some results on (total) domination number, (total) 2-domination number, (total) cobondage number and (total) 2-cobondage number. Finally, one of their applications related to location map of Fire Stations and Emergency Medical centers in urban regions of ​​a metropolis is presented.

Equitable Domination in Vague Graphs With Application in Medical Sciences

Considering all physical, biological, and social systems, fuzzy graph (FG) models serve the elemental processes of all natural and artificial structures. As the indeterminate information is an essential real-life problem, which is mostly uncertain, modeling the problems based on FGs is highly demanding for an expert. Vague graphs (VGs) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which FGs possibly will not succeed in bringing about satisfactory results. In addition, VGs are a very useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, medical science, and traffic plan. The previous definition restrictions in FGs have made us present new definitions in VGs. A wide range of applications has been attributed to the domination in graph theory for several fields such as facility location problems, school bus routing, modeling biological networks, and coding theory. Concepts from domination also exist in problems involving finding the set of representatives, in monitoring communication and electrical networks, and in land surveying (e.g., minimizing the number of places a surveyor must stand in order to take the height measurement for an entire region). Hence, in this article, we introduce different concepts of dominating, equitable dominating, total equitable dominating, weak (strong) equitable dominating, equitable independent, and perfect dominating sets in VGs and also investigate their properties by some examples. Finally, we present an application in medical sciences to show the importance of domination in VGs.

Some Operations on Complex Vague Graphs with Application

Vague graphs has found its importance in most recent years. It has played the vital role in many real life applications. The mathematical approach of blending different aspects of vague graphs gives a more generalized approach. As a result of it, we introduce the concepts of Complex vague graphs (CVG). In this chapter, we introduce certain notions including union, join, complement and composition of complex vague graphs. This helps in manipulating the real life applications in decision making problems. We also investigate on the ideas of homomorphisms of complex vague graphs. Finally we provide an application of CVG in launching a water reservoir in different locations.

Median vertex vague labeling of vague graphs

Median vertex vague labeling of vague graphs

Certain Concepts of Vague Graphs With Applications to Medical Diagnosis

Graphs are among the more ubiquitous models of natural and human-made structures. They are used to model with various categories of relations and process dynamics in biological and social systems. A vague graph has numerous applications in the fields of geometry and operational research. It has been a useful scope in various fields of computer science. In this paper, our important purpose of the study is to describe properties rejection, maximal product, symmetric difference and residue product of vague graphs which have been deeply discussion with different examples and moreover, we investigate some of their other related properties. We also presented the applications of vague set in medical diagnosis.