Intuitionistic Fuzzy Graphs Research Articles

New Concepts in Intuitionistic Fuzzy Graph with Application in Water Supplier Systems

In recent years, the concept of domination has been the backbone of research activities in graph theory. The application of graphic domination has become widespread in different areas to solve human-life issues, including social media theories, radio channels, commuter train transportation, earth measurement, internet transportation systems, and pharmacy. The purpose of this paper was to generalize the idea of bondage set (BS) and non-bondage set (NBS), bondage number α(G), and non-bondage number αk(G), respectively, in the intuitionistic fuzzy graph (IFG). The BS is based on a strong arc (SA) in the fuzzy graph (FG). In this research, a new definition of SA in connection with the strength of connectivity in IFGs was applied. Additionally, the BS, α(G), NBS, and αk(G) concepts were presented in IFGs. Three different examples were described to show the informative development procedure by applying the idea to IFGs. Considering the examples, some results were developed. Also, the applications were utilized in water supply systems. The present study was conducted to make daily life more useful and productive.

An Approach Towards Decision-Making and Shortest Path Problems Based on T-Spherical Fuzzy Information

In this paper, we propose some developments in fuzzy graph theory. An original notion of a T-spherical fuzzy graph is presented as a commonality of fuzzy graph, an intuitionistic fuzzy graph and a picture fuzzy graph. The originality, the imperativeness and the importance of this notion are discussed by showing some results, giving examples and graphical analysis. Some theoretical terms of graphs such as a T-spherical fuzzy subgraph, a complement of T-SFG, degree of T-SFG are clarified and their attributes and aspects are analyzed. Interestingly, three types of decision-making problems using the framework of T-SFGs are studied. These problems include the problem of the shortest path, the safe root for an airline journey and the problem of supply chain management in a T-spherical fuzzy network. The comparison of this new approach towards these problems with existing approaches is also established. A new algorithm is put forward in the event of T-SFGs and is used to seek out the shortest path problem. The overall analysis of the suggested notion under the prevailing theory is conducted. The advantages of the proposed approach are discussed based on the existing tools and a short comparison of the new with existing tools is established.

Bipolar Intuitionistic Fuzzy Graphs and its Matrices

Bipolar Intuitionistic Fuzzy Graphs and its Matrices

On lexicographic products of two intuitionistic fuzzy graphs

In this paper, lexicographic products of two intuitionistic fuzzy graphs, namely, lexicographic min product and lexicographic max product which are analogous to the concept lexicographic product in crisp graph theory are defined. It is illustrated that the operations lexicographic products are not commutative. The connected effective and complete properties of the operations lexicographic products are studied. The degree of a vertex in the lexicographic products of two intuitionistic fuzzy graph is obtained. A relationship between the lexicographic min product and lexicographic max–product is also obtained.

A study on regular picture fuzzy graph with applications in communication networks

Picture fuzzy graph (PFG) is an extended version of intuitionistic fuzzy graph (IFG) to model the uncertain real world problems, in which IFG may fail to model those problems properly. PFG is more precise, flexible and compatible than IFG to deal the real-life scenarios which consists of information these types: yes, abstain, no and refusal. The main focus of our study is to present the concept of isomorphic PFG, regular PFG (RPFG) and picture fuzzy multigraph. In this paper, we present the notation of RPFG. Many different types of RPFGs such as regular strong PFG, regular complete PFG, complete bipartite PFG and regular complement PFG are introduced. We also describe the concepts of dn and tdn-degree of a vertex in a RPFG. Based on those two types of degrees, we classify the regularity of PFG into 3 type’s namely, dn- RPFG, tdn-RPFG and n- highly irregular PFG. Several theorems of those RPFG are presented here. We define the busy vertex and free vertex in a RPFG. We present the notations of μ-complement, homomorphism, isomorphism, weak isomorphism and co weak isomorphism of RPFG. Some significant theorems on isomorphism and μ- complement of RPFG are derived here. We also introduce the notation of picture fuzzy multigraph. We present a mathematical model of communication network and transportation network by using picture fuzzy multigraph and real time data are collected so that the transportation network/communication network can work efficiently.

Intuitionistic L-fuzzy graph

In this paper we introduce intuitionistic L-fuzzy graph as a generalization of intuitionistic fuzzy graph. The operations on intuitionistic L-fuzzy graph such as union, intersection, complement are discussed. Also, we try to define matrices associated with Intuitionistic L-fuzzy graph.

Degree of a Vertex in Max-Product of Intuitionistic Fuzzy Graph

Graph theory has applications in many areas of computer science, including data mining, image segmentation, clustering and networking. Product on graphs has a wide range of application in networking system, automata theory, game theory and structural mechanics. In many cases, some aspects of a graph-theoretic problem may be uncertain. Intuitionistic fuzzy models provide more compatible to the system compared to the fuzzy models. An intuitionistic fuzzy graph can be derived from two given intuitionistic fuzzy graphs using max-product. In this paper, we studied the degree of vertex in intuitionistic fuzzy graph by the max-product of two given intuitionistic fuzzy graph. Also find the necessary and sufficient condition for max-product of two intuitionistic fuzzy graphs to be regular.

Perfectly Regular and Perfectly Edge-Regular Intuitionistic Fuzzy Graphs

A Perfectly regular intuitionistic fuzzy graph is an intuitionistic fuzzy graph that is both regular and totally regular. In this paper we introduce and classify these types of intuitionistic fuzzy graphs and study several of their properties, including how two classes of intuitionistic fuzzy graphs structurally relate to one another and several of their spectral properties such as isospectral intuitionistic fuzzy graphs and when the energy of intuitionistic fuzzy graph is proportional to the energy of their underlying crisp graphs. These properties are studied in particular due to having at least one constant function and .

Novel concepts in intuitionistic fuzzy graphs with application

Novel concepts in intuitionistic fuzzy graphs with application

Signless Laplacian Energy in Products of Intuitionistic Fuzzy Graphs

The observation of an Intuitionistic Fuzzy Graph’s signless laplacian energy is expanded innumerous products in Intuitionistic Fuzzy Graph. During this paper, we have got the value of signless laplacian Energy in unrelated products such as Cartesian product, Lexicographic Product, Tensor product and Strong Product, product, product and product amongst 2 intuitionistic Fuzzy graphs. Additionally we tend to study the relation between the Signless laplacian Energy within the varied products in 2 Intuitionistic Fuzzy Graphs.

Graph of an Intuitionistic Fuzzy Ideal of M⟙ Groups in Near Rings

The objective of this paper is to establish a relationship between intuitionistic fuzzy (IF) theory, graph theory, intuitionistic fuzzy graph theory with the ideal algebraic structure of a near ring in MΓ group. The idea of graph of an intuitionistic fuzzy (IF) ideal, the regular graph of an intuitionistic fuzzy (IF) ideal and their isomorphism in MΓ group of near rings are discussed. Also, few properties of theirs are studied here as theorems

Bounds for the Real and Complex Eigen Values of Energy of the Dominating Intuitionistic Fuzzy Graph

We define the dominating energy for an intuitionistic fuzzy directed graph and we derive the upper and lower bounds with real and complex eigenvalues for the energy of dominating intuitionistic fuzzy graph.

Pythagorean Dombi fuzzy graphs

Pythagorean fuzzy graph, a broadly used extension of fuzzy and intuitionistic fuzzy graph, is helpful in representing structural relationships between several objects where the relation between these objects is vague, while the Dombi operators with operational parameters have excellent flexibility. Utilizing these two concepts, this research paper proposes the novel concept of Pythagorean Dombi fuzzy graphs (PDFGs). Basically, graph terminology is employed for introducing Pythagorean fuzzy analogs of various fundamental graphical ideas using Dombi operator. Further, under Pythagorean Dombi fuzzy environment, regular, totally regular, strongly regular and biregular graphs are defined with appropriate illustration and some of their crucial properties are examined. Meanwhile, the notion of edge regularity of PDFG is also initiated with substantial characteristics. Finally, a numerical example related to evaluation of appropriate ETL software for a business intelligence project is presented to better understand PDFGs.

Product Operations on q-Rung Orthopair Fuzzy Graphs

The q-rung orthopair fuzzy graph is an extension of intuitionistic fuzzy graph and Pythagorean fuzzy graph. In this paper, the degree and total degree of a vertex in q-rung orthopair fuzzy graphs are firstly defined. Then, some product operations on q-rung orthopair fuzzy graphs, including direct product, Cartesian product, semi-strong product, strong product, and lexicographic product, are defined. Furthermore, some theorems about the degree and total degree under these product operations are put forward and elaborated with several examples. In particular, these theorems improve the similar results in single-valued neutrosophic graphs and Pythagorean fuzzy graphs.

Intuitionistic fuzzy graphs of nth type with applications

Intuitionistic fuzzy graphs of nth type with applications

Constant single valued neutrosophic graphs with applications

In this paper, we introduced a new concept of a single-valued neutrosophic graph (SVNG) known as a constant single-valued neutrosophic graph (CSVNG). Basically, SVNG is a generalization of intuitionistic fuzzy graph (IFG). More specifically, we described and explored some graph-theoretic ideas related to the introduced concepts of CSVNG. An application of CSVNG in a Wi-Fi network system is discussed and a comparison of CSVNG with constant IFG is established showing the worth of the proposed work. Further, several terms like constant function and totally constant function are investigated in the framework of CSVNG and their characteristics are studied.

Complex Intuitionistic Fuzzy Graphs with Application in Cellular Network Provider Companies

In recent years, a mathematical approach of blending different aspects is on the way, which as a result gives a more generalized approach. Following the above mathematical approach, we combine two very powerful techniques, namely complex intuitionistic fuzzy sets and graph theory, and introduce the notion of complex intuitionistic fuzzy graphs. Then, we introduce certain notions including union, join and composition of complex intuitionistic fuzzy graphs, through which one can easily manipulate the complex intuitionistic fuzzy graphs in decision making problems. We elucidate these operations with some examples. We also describe the homomorphisms of complex intuitionistic fuzzy graphs. Finally, we provide an application in cellular network provider companies for the testing of our approach.

Some composition properties on totally regular intuitionistic fuzzy graphs

Some composition properties on totally regular intuitionistic fuzzy graphs

Dominating Energy of Operations on Intuitionistic Fuzzy Graphs

The concept of energy of an Intuitionistic Fuzzy Graph is extended to dominating Energy in operations on Intuitionistic Fuzzy Graph. In this paper, We have obtained the value of dominating Energy in different operations such as complement, Union, Join, Cartesian product and composition between two intuitionistic Fuzzy graphs. Also we study the relation between the dominating Energy in the operations on two Intuitionistic Fuzzy Graphs.

An Intuitionistic Fuzzy Graph’s Signless Laplacian Energy

We are extending concept into the Intuitionistic fuzzy graph’ Signless Laplacian energy instead of the Signless Laplacian energy of fuzzy graph. Now we demarcated an Intuitionistic fuzzy graph’s Signless adjacency matrix and also an Intuitionistic fuzzy graph’s Signless Laplacian energy. Here we find the Signless Laplacian energy ‘s Intuitionistic fuzzy graphs above and below boundaries of an with suitable examples.