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Journal articles on the topic 'Degree of a vertex in an intuitionistic fuzzy graph'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

P., Karthick. "Some Classes on Product of Intuitionistic Fuzzy Graphs." Journal of Applied Mathematics and Statistical Analysis 1, no. 2 (2020): 1–8. https://doi.org/10.5281/zenodo.4067900.

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<em>Intuitionistic fuzzy graph is a generalization of a fuzzy graph. The purpose of this research paper is to calculate the degree of the vertices for an intuitionistic fuzzy graphs. This IFGs are derived from given intuitionistic fuzzy graphs based on the operators cartesian product, composition and tensor product</em>

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2

Yin, Songyi, Hongxu Li, and Yang Yang. "Product Operations on q-Rung Orthopair Fuzzy Graphs." Symmetry 11, no. 4 (2019): 588. http://dx.doi.org/10.3390/sym11040588.

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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 r

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3

Anwar, Abida, and Faryal Chaudhry. "On Certain Products of Complex Intuitionistic Fuzzy Graphs." Journal of Function Spaces 2021 (December 16, 2021): 1–9. http://dx.doi.org/10.1155/2021/6515646.

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A complex intuitionistic fuzzy set (CIFS) can be used to model problems that have both intuitionistic uncertainty and periodicity. A diagram composed of nodes connected by lines and labeled with specific information may be used to depict a wide range of real-life and physical events. Complex intuitionistic fuzzy graphs (CIFGs) are a broader type of diagram that may be used to manipulate data. In this paper, we define the key operations direct, semistrong, strong, and modular products for complex intuitionistic fuzzy graphs and look at some interesting findings. Further, the strong complex intu

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4

Parimala, Mani, Arwa Almunajam, Muthusamy Karthika, and Ibtesam Alshammari. "Pythagorean Fuzzy Digraphs and Its Application in Healthcare Center." Journal of Mathematics 2021 (September 6, 2021): 1–6. http://dx.doi.org/10.1155/2021/5459654.

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The notion of fuzzy set is introduced to deal with uncertainty, whereas the conventional sets are used for certainty. The extensions of fuzzy set theory such as intuitionistic fuzzy set (IFS) and Pythagorean fuzzy sets (PyFS) were introduced to overcome drawbacks in fuzzy theory. Fuzzy graph structure is used to deal with the uncertainty in a network and describe its relation on the nonempty vertex set. One of the extensions of intuitionistic fuzzy digraph (IFDG) is Pythagorean fuzzy digraph (PyFDG). IFDG cannot handle if the sum of degree of acceptance and degree of rejection for an arc weigh

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Shoaib, Muhammad, Waqas Mahmood, Weded Albalawi, and Faria Ahmad Shami. "Notion of Complex Spherical Fuzzy Graph with Application." Journal of Function Spaces 2022 (May 18, 2022): 1–27. http://dx.doi.org/10.1155/2022/1795860.

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A complex spherical fuzzy set (CSFS) is a generalization of a spherical fuzzy set (CFS). CSFS handles vagueness more explicitly, and its range is expanded from the real subset to the complex with unit disc. The major goal of this research is to present the foundation of a complex spherical fuzzy graph (CSFG) due to the limitation of the complex neutral membership function in a complex Pythagorean fuzzy graph (CPFG). Complex spherical fuzzy models have more flexibility as compared to complex fuzzy models, complex intuitionistic fuzzy models, and complex Pythagorean fuzzy models due to their cov

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6

Tola, Keneni Abera, V. N. Srinivasa Rao Repalle, and Mamo Abebe Ashebo. "Theory and Application of Interval-Valued Neutrosophic Line Graphs." Journal of Mathematics 2024 (March 19, 2024): 1–17. http://dx.doi.org/10.1155/2024/5692756.

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Neutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interval-valued neutrosophic graphs (IVNGs) were defined. The interval-valued neutrosophic graph is a fundamental issue in graph theory that has wide applications in the real world. Also, problems may arise when partial ignorance exists in the datasets of membership [0, 1], and then, the concept of IVNG is

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7

Xiao, Wei, Arindam Dey, and Le Hoang Son. "A study on regular picture fuzzy graph with applications in communication networks." Journal of Intelligent & Fuzzy Systems 39, no. 3 (2020): 3633–45. http://dx.doi.org/10.3233/jifs-191913.

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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, comple

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Nazir, Nazia, Tanzeela Shaheen, LeSheng Jin, and Tapan Senapati. "An Improved Algorithm for Identification of Dominating Vertex Set in Intuitionistic Fuzzy Graphs." Axioms 12, no. 3 (2023): 289. http://dx.doi.org/10.3390/axioms12030289.

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In graph theory, a “dominating vertex set” is a subset of vertices in a graph such that every vertex in the graph is either a member of the subset or adjacent to a member of the subset. In other words, the vertices in the dominating set “dominate” the remaining vertices in the graph. Dominating vertex sets are important in graph theory because they can help us understand and analyze the behavior of a graph. For example, in network analysis, a set of dominant vertices may represent key nodes in a network that can influence the behavior of other nodes. Identifying dominant sets in a graph can al

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9

Myithili, K. K., and P. Nithyadevi. "Degrees and regularity of intuitionistic fuzzy semihypergraphs." Notes on Intuitionistic Fuzzy Sets 31, no. 1 (2025): 111–26. https://doi.org/10.7546/nifs.2025.31.1.111-126.

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This research work takes a new paradigm on the hypergraph concept which is a combination of a hypergraph and a semigraph. A semihypergraph is a connected hypergraph in which each hyperedge must have at least three vertices and any two hyperedges have at least one vertex in common. In a semihypergraph, vertices are classified as end, middle or middle-end vertices. This distinction, combined with membership and non-membership values, enables a more granular examination of vertices and their degrees in Intuitionistic Fuzzy Semihypergraphs (IFSHGs). This paper proposes four types of degrees: degre

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Isnaini Rosyida. "On Strong Fuzzy Resolving Set of Fuzzy Wheel Graphs." Advances in Nonlinear Variational Inequalities 28, no. 5s (2025): 132–39. https://doi.org/10.52783/anvi.v28.3655.

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Let Image be a fuzzy set on Image. A fuzzy labeling graph Image is a graph with bijective membership functions Image and Image so that each vertex’s membership degree and every edge’s membership value are different. Further, it satisfies Image for Image. “A graph formed from a single vertex connected to the vertices of a cycle of length Image is called a wheel graph with Image vertices". In this paper, we construct an algorithm for fuzzy labeling of wheel graphs. Under the algorithm, we have the degrees of vertices and edges are different and the monotone decreasing. The vertex Image gets the

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11

S.Revathi, C. V. R. Harinarayanan, and R.Muthuraj. "Perfect Domination in Constant Intuitionistic Fuzzy Graph of Degree (ki ,kj)." International Journal of Fuzzy Mathematical Archive 14, no. 01 (2017): 91–99. http://dx.doi.org/10.22457/ijfma.v14n1a11.

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In this paper, the new kind of parameter perfect dominating set in constant intuitionistic fuzzy graph is defined and established the parametric conditions. Another new kind of parameter totally constant intuitionistic fuzzy graph is defined and established the parametric conditions. Some properties of Perfect dominating set in constant IFG and totally constant IFG with suitable examples are also discussed.

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12

Khan, Sami Ullah, Naeem Jan, Kifayat Ullah, and Lazim Abdullah. "Graphical Structures of Cubic Intuitionistic Fuzzy Information." Journal of Mathematics 2021 (May 11, 2021): 1–21. http://dx.doi.org/10.1155/2021/9994977.

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The theory developed in this article is based on graphs of cubic intuitionistic fuzzy sets (CIFS) called cubic intuitionistic fuzzy graphs (CIFGs). This graph generalizes the structures of fuzzy graph (FG), intuitionistic fuzzy graph (IFG), and interval-valued fuzzy graph (IVFG). Moreover, several associated concepts are established for CIFG, such as the idea subgraphs, degree of CIFG, order of CIFG, complement of CIFG, path in CIFG, strong CIFG, and the concept of bridges for CIFGs. Furthermore, the generalization of CIFG is proved with the help of some remarks. In addition, the comparison am

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13

James, Josna, and Shiny Jose. "Effective Edge Domination in iterated Jump Graph of Intuitionistic Fuzzy Graph." Mapana Journal of Sciences 23, no. 2 (2024): 151–62. https://doi.org/10.12723/mjs.69.9.

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Intuitionistic Fuzzy Graphs (InFGs) serve as a sophisticated framework for modeling complex and uncertain phenomena across diverse domains, such as decision-making, economics, medicine, computer science, and engineering. In this research, we develop and analyse the properties of jump graphs in the context of InFGs. The vertex set of the jump graph J(G) of a graph G is defined as the edge set of G, with adjacency between vertices in J(G) established if and only if the corresponding edges in G are non-incident. We systematically construct sequences of jump graphs for InFGs through iterative proc

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14

Talaee, B., and G. Nasiri. "On intersection graph of intuitionistic fuzzy submodules of a module." Lebanese Science Journal 20, no. 1 (2019): 104–21. http://dx.doi.org/10.22453/lsj-020.1.104-121.

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There are some interesting relations between submodules of a module and its intuitionistic fuzzy (IF) submodules. In this paper we investigate some relationshipsbetween submodules of a module and its IFsubmodules. Then we introduce a graph structure on IFsubmodules of a module and obtain some properties of it, that is the main goal of this paper. We define the intersection graph of submodules of a module M(G) and we show that a submodule Nof Mis a center in MGif and only if IFNis a center in IFG. We get some relationships between IFsubmodules of a module and their supports, as vertices o

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15

Kolandasamy, Renuka, D. Ramesh, Aiyared Iampan, Gadde Sambasiva Rao, Sravani Jayanti, and Sabenabanu Abdulkadhar. "Regular Fuzzy Graphs with Chromatic Numbers." International Journal of Analysis and Applications 23 (July 16, 2025): 173. https://doi.org/10.28924/2291-8639-23-2025-173.

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Let G = (σ, µ) be a fuzzy graph on G∗ = (V, E). If each vertex in G has the same degree k, then G is said to be a vertex regular fuzzy graph or a k-vertex regular fuzzy graph. The minimum number of colors required to color all the vertices in such a way that no two adjacent vertices receive the same color is called the chromatic number and is denoted by χ(G). In this paper, we present results based on cubic graphs and their chromatic number with regular fuzzy graphs, which are briefly denoted by fr(G).

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16

Al-Masarwah, Anas, and Majdoleen Abu Qamar. "Certain Types of Fuzzy Soft Graphs." New Mathematics and Natural Computation 14, no. 02 (2018): 145–56. http://dx.doi.org/10.1142/s1793005718500102.

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In this paper, we introduce the concepts of uniform vertex fuzzy soft graphs, uniform edge fuzzy soft graphs, degree of a vertex, total degree of a vertex and complement fuzzy soft graphs with some examples. Also, we study regular and totally regular fuzzy soft graphs, and the conditions under which the complement of regular fuzzy soft graph becomes regular as well as totally regular are discussed. Also, we obtain some results related to regular, totally regular and complete fuzzy soft graphs.

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17

Sitara, Muzzamal, Muhammad Akram, and Muhammad Yousaf Bhatti. "Fuzzy Graph Structures with Application." Mathematics 7, no. 1 (2019): 63. http://dx.doi.org/10.3390/math7010063.

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In this article, we introduce the notions of maximal products of fuzzy graph structures, regular fuzzy graph structures, and describe these notions with examples and properties. Further, we present the degree and total degree of a vertex in maximal product of fuzzy graph structures and explain some of their properties. Furthermore, we develop a flowchart to show general procedure of application of fuzzy graph structure, regarding identification of most controversial issues among countries.

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18

Kang, Kyung Tae, Seok-Zun Song, and Young Bae Jun. "Multipolar Intuitionistic Fuzzy Set with Finite Degree and Its Application in BCK/BCI-Algebras." Mathematics 8, no. 2 (2020): 177. http://dx.doi.org/10.3390/math8020177.

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When events occur in everyday life, it is sometimes advantageous to approach them in two directions to find a solution for them. As a mathematical tool to handle these things, we can consider the intuitionistic fuzzy set. However, when events are complex and the key to a solution cannot be easily found, we feel the need to approach them for hours and from various directions. As mathematicians, we wish we had the mathematical tools that apply to these processes. If these mathematical tools were developed, we would be able to apply them to algebra, topology, graph theory, etc., from a close poin

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19

Nisha., D., and B. Srividhya. "Characteristics of Fuzzy Wheel Graph and Hamilton Graph with Fuzzy Rule." International Journal of Trend in Scientific Research and Development 3, no. 6 (2019): 1061–64. https://doi.org/10.5281/zenodo.3589329.

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Graph theory is the concepts used to study and model various application in different areas. We proposed the wheel graph with n vertices can be defined as 1 skeleton of on n 1 gonal pyramid it is denoted by w nwith n 1 vertex n=3 . A wheel graph is hamiltonion, self dual and planar. In the mathematical field of graph theory, and a Hamilton path or traceable graph is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle is a hamiltonian path that is a cycle. In this paper, we consider the wheel graph and also the hamilton graph using if then rules f

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20

Alanazi, Abdulaziz M., Ghulam Muhiuddin, Bashair M. Alenazi, Tanmoy Mahapatra, and Madhumangal Pal. "Utilizing m-Polar Fuzzy Saturation Graphs for Optimized Allocation Problem Solutions." Mathematics 11, no. 19 (2023): 4136. http://dx.doi.org/10.3390/math11194136.

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It is well known that crisp graph theory is saturated. However, saturation in a fuzzy environment has only lately been created and extensively researched. It is necessary to consider m components for each node and edge in an m-polar fuzzy graph. Since there is only one component for this idea, we are unable to manage this kind of circumstance using the fuzzy model since we take into account m components for each node as well as edges. Again, since each edge or node only has two components, we are unable to apply a bipolar or intuitionistic fuzzy graph model. In contrast to other fuzzy models,

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21

Radha, K., and S. R. Gayathri. "Distance Degree Sequence and Distance Neighborhood Degree Sequence of Vertices in Fuzzy Graphs and Some of Their Properties." Indian Journal Of Science And Technology 17, no. 41 (2024): 4349–57. http://dx.doi.org/10.17485/ijst/v17i41.1933.

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Objectives: The objective of this study is to explore new types of sequences in fuzzy graphs namely distance degree sequence and distance neighborhood degree sequence of fuzzy graphs which may have various applications in the real world. Methods: In this paper, two unique sequences for each vertex of fuzzy graphs are given by means of its degree and neighborhood degree which are called as the distance degree sequence and distance neighborhood degree sequence of vertices of fuzzy graphs respectively. The n-tuple of the distance degree sequence of vertices of a fuzzy graph arranged in lexicograp

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22

Kumaran, Narayanan, Annamalai Meenakshi, Miroslav Mahdal, Jayavelu Udaya Prakash, and Radek Guras. "Application of Fuzzy Network Using Efficient Domination." Mathematics 11, no. 10 (2023): 2258. http://dx.doi.org/10.3390/math11102258.

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Let Heff (Veff, Eeff) be a finite simple connected graph of order m with vertex set Veff and edge set Eeff. A dominating set Sds⊆Veff is called an efficiently dominating set if, for every vertex ua∈VG, NGua∩Sds=1—where NG [ua] denotes the closed neighborhood of the vertex ua. Using efficient domination techniques and labelling, we constructed the fuzzy network. An algorithm has been framed to encrypt and decrypt the secret information present in the network, and furthermore, the algorithm has been given in pseudocode. The mathematical modelling of a strong fuzzy network is defined and construc

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23

Koam, Ali N. A., Muhammad Akram, and Peide Liu. "Decision-Making Analysis Based on Fuzzy Graph Structures." Mathematical Problems in Engineering 2020 (August 12, 2020): 1–30. http://dx.doi.org/10.1155/2020/6846257.

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A graph structure is a useful framework to solve the combinatorial problems in various fields of computational intelligence systems and computer science. In this research article, the concept of fuzzy sets is applied to the graph structure to define certain notions of fuzzy graph structures. Fuzzy graph structures can be very useful in the study of various structures, including fuzzy graphs, signed graphs, and the graphs having labeled or colored edges. The notions of the fuzzy graph structure, lexicographic-max product, and degree and total degree of a vertex in the lexicographic-max product

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24

K, Radha, and R. Gayathri S. "Distance Degree Sequence and Distance Neighborhood Degree Sequence of Vertices in Fuzzy Graphs and Some of Their Properties." Indian Journal of Science and Technology 17, no. 41 (2024): 4349–57. https://doi.org/10.17485/IJST/v17i41.1933.

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Abstract <strong>Objectives:</strong> The objective of this study is to explore new types of sequences in fuzzy graphs namely distance degree sequence and distance neighborhood degree sequence of fuzzy graphs which may have various applications in the real world. <strong>Methods:</strong> In this paper, two unique sequences for each vertex of fuzzy graphs are given by means of its degree and neighborhood degree which are called as the distance degree sequence and distance neighborhood degree sequence of vertices of fuzzy graphs respectively. The n-tuple of the distance degree se

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25

Ismayil, A. Mohamed, and S. Syed Asad Ahmed. "Degree, Neighbourhood, and Connectedness in Fuzzy Digraph." Indian Journal Of Science And Technology 17, no. 44 (2024): 4571–81. https://doi.org/10.17485/ijst/v17i44.3556.

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Objective: In the context of fuzzy digraphs, degree neighborhood, and connectedness play important roles in understanding the structure and relationships within the graph. Here are the objectives of degree, neighborhood, and connectedness in fuzzy digraphs: 1. Degree Neighborhood: The degree neighborhood of a vertex in a fuzzy digraph refers to the set of vertices that are directly connected to it. In fuzzy digraphs, the concept of degree neighborhood is extended to include the strength or degree of connection between vertices, which is represented by fuzzy values. 2. Connectedness: Connectedn

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26

V., Ramadoss, and Kalpana D. "A SURVEY OF HYPO SOFT GRAPH STRUCTURES." International Journal of Applied and Advanced Scientific Research 3, no. 1 (2018): 159–64. https://doi.org/10.5281/zenodo.1193685.

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Akram [2] introduced the concept of bipolar fuzzy graphs and defined different operations on it. A. Nagoorgani and K. Radha [3, 4] introduced the concept of regular fuzzy graphs in 2008 and discussed about the degree of a vertex in some fuzzy graphs. K. Radha and N. Kumaravel [5] introduced the concept of edge degree, total edge degree and discussed about the degree of an edge in some fuzzy graphs. S. Arumugam and S. Velammal [6] discussed edge domination in fuzzy graphs. Soft set theory was introduced by Molodtsov [9] for modelling vagueness and uncertainty and it has been received much atten

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27

Garai, Arindam, and Tapan Kumar Roy. "Intuitionistic Fuzzy Modeling to Travelling Salesman Problem." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 11, no. 9 (2013): 3015–24. http://dx.doi.org/10.24297/ijct.v11i9.3414.

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This paper presents solution technique for travelling salesman problem (TSP) under intuitionistic fuzzy environment. Travelling salesman problemÂ is a non-deterministic polynomial-time (NP) hardÂ problem inÂ combinatorial optimization,Â studied inÂ graph theory, operations researchÂ andÂ theoretical computer science. It must be noted that a traveling sales man even face a situation in which he is not able to achieve his objectives completely. There must be a set of alternatives from which he can select one that best meets his aspiration level. For Multi-Objective Symmetric TSP, in fuzzy enviro

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28

A, Mohamed Ismayil, and Syed Asad Ahmed S. "Degree, Neighbourhood and Connectedness in Fuzzy Digraph." Indian Journal of Science and Technology 17, no. 44 (2024): 4571–81. https://doi.org/10.17485/IJST/v17i44.3556.

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Abstract <strong>Objective:</strong> In the context of fuzzy digraphs, degree neighborhood, and connectedness play important roles in understanding the structure and relationships within the graph. Here are the objectives of degree, neighborhood, and connectedness in fuzzy digraphs: 1. Degree Neighborhood: The degree neighborhood of a vertex in a fuzzy digraph refers to the set of vertices that are directly connected to it. In fuzzy digraphs, the concept of degree neighborhood is extended to include the strength or degree of connection between vertices, which is represented by fuzzy value

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29

Indumathi, P., S. Santhosh Kumar, R. ,. Buvaneswari, and S. K. Mala. "Total degree of maximal product of two constant intuitionistic fuzzy graphs." Edelweiss Applied Science and Technology 8, no. 6 (2024): 5789–99. http://dx.doi.org/10.55214/25768484.v8i6.3258.

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This paper explains about the Total degree of Maximal product of Two constant IF graphs. Fuzzy graphs are derived from crisp graphs. Various properties of IF graphs are extended from Fuzzy graphs. Maximal product of Fuzzy graph structures with applications have been discussed in different papers and extended to IF graphs. Constant IF graphs are special type of IF graphs which have same degree for all its vertices. IF Graphs have many applications including the investigation of images by image segmentation, Brain mapping etc, Maximal product of fuzzy graphs is applied in various fields like eff

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30

Shoaib, Muhammad, Waqas Mahmood, Ahmad N. Al-Kenani, and Sahidul Islam. "Notes on Upper and Lower Truncation of Picture Fuzzy Graphs." Discrete Dynamics in Nature and Society 2022 (April 26, 2022): 1–11. http://dx.doi.org/10.1155/2022/7646828.

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Due to the absence of a neutral function, there are drawbacks to the existing definition of an intuitionistic fuzzy graph (Int-FG). In that definition of Int-FG, membership function and nonmembership function are involved. In this study, lower truncation (Low-T) and upper truncation (Up-T) are applied to picture fuzzy graphs (Pic-FGs). Pic-FG has an additional neutral membership function. Furthermore, Low-T and Up-T of subdivision of the picture fuzzy line graph (Pic-FLnG) are also discussed. The degree of an edge in both Up-T and Low-T of Pic-FG is discussed. Some related theorems related to

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31

Shoaib, Muhammad, Waqas Mahmood, Ahmad N. Al-Kenani, and Sahidul Islam. "Notes on Upper and Lower Truncation of Picture Fuzzy Graphs." Discrete Dynamics in Nature and Society 2022 (April 26, 2022): 1–11. http://dx.doi.org/10.1155/2022/7646828.

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Due to the absence of a neutral function, there are drawbacks to the existing definition of an intuitionistic fuzzy graph (Int-FG). In that definition of Int-FG, membership function and nonmembership function are involved. In this study, lower truncation (Low-T) and upper truncation (Up-T) are applied to picture fuzzy graphs (Pic-FGs). Pic-FG has an additional neutral membership function. Furthermore, Low-T and Up-T of subdivision of the picture fuzzy line graph (Pic-FLnG) are also discussed. The degree of an edge in both Up-T and Low-T of Pic-FG is discussed. Some related theorems related to

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32

Cai, Ruiqi, Buvaneswari Rangasamy, Senbaga Priya Karuppusamy, and Aysha Khan. "Characterization of Degree Energies and Bounds in Spectral Fuzzy Graphs." Symmetry 17, no. 5 (2025): 644. https://doi.org/10.3390/sym17050644.

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This study explores the degree energy of fuzzy graphs to establish fundamental spectral bounds and characterize adjacency structures. We derive upper bounds on the sum of squared degree eigenvalues based on vertex degree distributions and formulate constraints using the characteristic polynomial of the maximum degree matrix. Furthermore, we demonstrate that the average degree energy of a connected fuzzy graph remains strictly positive. The proposed framework is applied to protein–protein interaction networks, identifying critical proteins and enhancing network resilience analysis.

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Kausar, Andleeb, Nabilah Abughazalah, and Naveed Yaqoob. "Multi Polar q-Rung Orthopair Fuzzy Graphs with Some Topological Indices." Symmetry 15, no. 12 (2023): 2131. http://dx.doi.org/10.3390/sym15122131.

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The importance of symmetry in graph theory has always been significant, but in recent years, it has become much more so in a number of subfields, including but not limited to domination theory, topological indices, Gromov hyperbolic graphs, and the metric dimension of graphs. The purpose of this monograph is to initiate the idea of a multi polar q-rung orthopair fuzzy graphs (m-PqROPFG) as a fusion of multi polar fuzzy graphs and q-rung orthopair fuzzy graphs. Moreover, for a vertex of multi polar q-rung orthopair fuzzy graphs, the degree and total degree of the vertex are defined. Then, some

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Rahayu, H. S., I. M. Sulandra, and V. Kusumasari. "Product of bipolar anti fuzzy graph and their degree of vertex." Journal of Physics: Conference Series 1872, no. 1 (2021): 012013. http://dx.doi.org/10.1088/1742-6596/1872/1/012013.

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35

Shoaib, Muhammad, Waqas Mahmood, Qin Xin, and Fairouz Tchier. "Maximal Product and Symmetric Difference of Complex Fuzzy Graph with Application." Symmetry 14, no. 6 (2022): 1126. http://dx.doi.org/10.3390/sym14061126.

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A complex fuzzy set (CFS) is described by a complex-valued truth membership function, which is a combination of a standard true membership function plus a phase term. In this paper, we extend the idea of a fuzzy graph (FG) to a complex fuzzy graph (CFG). The CFS complexity arises from the variety of values that its membership function can attain. In contrast to a standard fuzzy membership function, its range is expanded to the complex plane’s unit circle rather than [0,1]. As a result, the CFS provides a mathematical structure for representing membership in a set in terms of complex numbers. I

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P., Sinthamani. "Microscopic Examinations of the Elements on the Behaviour of Group of Fellow Men using Fuzzy Graph." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 3 (2020): 220–26. https://doi.org/10.35940/ijeat.B4533.029320.

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In this work, the behavior of an individual of a group to his fellow men. In a group, if we consider the relationship between people, we note the following possibilities. Any two of them may like each other or dislikes each other or indifferent to each other. It can be also checked originally to describe the way psychological consistency is obtained. And signed degree vertex evolves interesting results in new parameters of Balanced signed fuzzy graph and unbalanced signed fuzzy graph also we obtained some properties over it.

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S.N, Suber Bathusha, and S. Angelin Kavitha Raj. "Climatic analysis based on interval-valued complex Pythagorean fuzzy graph structure." Annals of Mathematics and Computer Science 19 (December 18, 2023): 10–33. http://dx.doi.org/10.56947/amcs.v19.213.

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The Interval-valued Complex Pythagorean Fuzzy Set (IVCPFS), an extension of the Pythagorean Fuzzy Set (PFS), offers a more accurate description of uncertainty than traditional fuzzy sets. It has numerous uses in fuzzy control. In this research study, we show the concept of Interval-Valued Complex Pythagorean Fuzzy Graph Structure (IVCPFGS), as well as the results of some regular IVCPFGS and totally regular IVCPFGS, along with the degree of vertex present. We also discussed the subdivision of an IVCPFGS, the complement IVCPFGS, and the strength of a Path in an IVCPFGS. Finally, we discuss a rea

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Renuka, Sahu, and Kumar Sharma Animesh. "Understanding the Unique Properties of Fuzzy Concept in Binary Trees." Indian Journal of Science and Technology 16, no. 33 (2023): 2631–36. https://doi.org/10.17485/IJST/v16i33.874.

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Abstract <strong>Objective:</strong> This study investigated the properties of fuzzy binaries, a type of rooted trees, and explored their implications in different domains. <strong>Method:</strong> This investigation included analyzing the structural properties of fuzzy binary tree, such as the number of vertices, the height, and the degree to which edges were assigned membership. Theorem: Combinatorial analysis and mathematical induction were used to derive the relation between the number of vertex and height of a fuzzy binary tree based on its internal vertex. The conditions t

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T, Bharathi, and Leo S. "A Study on Plithogenic Product Fuzzy Graphs with Application in Social network." Indian Journal of Science and Technology 14, no. 40 (2021): 3051–63. https://doi.org/10.17485/IJST/v14i40.1298.

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Abstract <strong>Objectives:</strong> The main objective of this study is to define Plithogenic product fuzzy graphs (PPFGs), and introduce its properties.<strong> Method:</strong> PPFGs is newly introduced as a new graphical model where P-vertices are characterized by four or more attributes and the attribute values of P-edges are computed using the product operator. Findings: Theoretical discussions and results related to PPFGs, and subgraphs, paths, cycles, trees, bridge and cut vertex in PPFGs are demonstrated with examples. A social network model based on the notion of PPFG

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Akram, Muhammad, Saba Siddique, and Majed G. Alharbi. "Clustering algorithm with strength of connectedness for $ m $-polar fuzzy network models." Mathematical Biosciences and Engineering 19, no. 1 (2021): 420–55. http://dx.doi.org/10.3934/mbe.2022021.

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<abstract><p>In this research study, we first define the strong degree of a vertex in an $ m $-polar fuzzy graph. Then we present various useful properties and prove some results concerning this new concept, in the case of complete $ m $-polar fuzzy graphs. Further, we introduce the concept of $ m $-polar fuzzy strength sequence of vertices, and we also investigate it in the particular instance of complete $ m $-polar fuzzy graphs. We discuss connectivity parameters in $ m $-polar fuzzy graphs with precise examples, and we investigate the $ m $-polar fuzzy analogue of Whitney's the

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Rosyida, Isnaini, and Suryono Suryono. "Coloring picture fuzzy graphs through their cuts and its computation." International Journal of Advances in Intelligent Informatics 7, no. 1 (2021): 63. http://dx.doi.org/10.26555/ijain.v7i1.612.

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In a fuzzy set (FS), there is a concept of alpha-cuts of the FS for alpha in [0,1]. Further, this concept was extended into (alpha,delta)-cuts in an intuitionistic fuzzy set (IFS) for delta in [0,1]. One of the expansions of FS and IFS is the picture fuzzy set (PFS). Hence, the concept of (alpha,delta)-cuts was developed into (alpha,delta,beta)-cuts in a PFS where beta is an element of [0,1]. Since a picture fuzzy graph (PFG) consists of picture fuzzy vertex or edge sets or both of them, we have an idea to construct the notion of the (alpha,delta,beta)-cuts in a PFG. The steps used in this pap

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Rao, Yongsheng, Saeed Kosari, Zehui Shao, Ruiqi Cai, and Liu Xinyue. "A Study on Domination in Vague Incidence Graph and Its Application in Medical Sciences." Symmetry 12, no. 11 (2020): 1885. http://dx.doi.org/10.3390/sym12111885.

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Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), have been acknowledged as being an applicable and well-organized tool to epitomize and solve many multifarious real-world problems in which vague data and information are essential. Owing to unpredictable and unspecified information being an integral component in real-life problems that are often uncertain, it is highly challenging for an expert to illustrate those problems through a fuzzy graph. Therefore, resolving the uncertainty accompanying the unpredictable and unspecified information of any real-world problem can be don

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V., Ramadass, and Kalpana D. "REPRESENTATIONS OF EDGE REGULAR BIPOLAR FUZZY GRAPHS." International Journal of Applied and Advanced Scientific Research 2, no. 2 (2017): 267–72. https://doi.org/10.5281/zenodo.1069074.

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V. Ramadass & D. Kalpana, “Representations of Edge Regular Bipolar Fuzzy Graphs”, International Journal of Applied and Advanced Scientific Research, Volume 2, Issue 2, Page Number 267-272, 2017.

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"Degree of a Vertex in Max-Product of Intuitionistic Fuzzy Graph." International Journal of Recent Technology and Engineering 8, no. 4 (2019): 2902–5. http://dx.doi.org/10.35940/ijrte.c6411.118419.

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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 intuitioni

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Mohamed, S. Yahya, and A. Mohamed Ali. "Complement of max product of intuitionistic fuzzy graphs." Complex & Intelligent Systems, July 27, 2021. http://dx.doi.org/10.1007/s40747-021-00438-2.

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AbstractIn this paper, the complement of max product of two intuitionistic fuzzy graphs is defined. The degree of a vertex in the complement of max product of intuitionistic fuzzy graph is studied. Some results on complement of max product of two regular intuitionistic fuzzy graphs are stated and proved. Finally, we provide an application of intuitionistic fuzzy graphs in school determination using normalized Hamming distance.

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M., Aslam Malik, Rashmanlou Hossein, Shoaib Muhammad, A. Borzooei R., Taheri Morteza, and Broumi Said. "A Study on Bipolar Single-Valued Neutrosophic Graphs With Novel Application." March 22, 2020. https://doi.org/10.5281/zenodo.3723630.

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Unipolar is less fundamental than bipolar cognition based on truth, and composure is a restraint for truth-based worlds. Bipolarity is the most powerful phenomenon that survives when truth disappeared in a black hole due to Hawking radiation or particular / anti particular emission. The purpose of this research study is to dene few four operations, including residue product, rejection, maximal product and symmetric difference of bipolar single-valued neutrosophic graph (BSVNG) and to explore some of their related properties with examples. Bipolar single-valued neutrosophic graph (BSVNG) is the

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S.Ravi, Narayanan. "2-Pseudo Neighbourly Irregular Intuitionistic Fuzzy Graphs." November 30, 2016. https://doi.org/10.5281/zenodo.826796.

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Shaik, Noorjahan, and Sharief Basha Shaik. "Wiener index application in intuitionistic fuzzy rough graphs for transport network flow." Scientific Reports 15, no. 1 (2025). https://doi.org/10.1038/s41598-025-94488-y.

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Abstract The applicability of different topological indices is indispensable in fields such as chemistry, electronics, economics, business studies, medicine, and the social sciences. The most popular index in graph theory is the wiener index $$\left(\mathcal{W}\mathcal{I}\right)$$ , which is based on the geodesic distance between two vertices. It is assumed that the weight of the geodesic between vertex x and vertex y in intuitionistic fuzzy rough graphs (IFRG) is zero in the absence of a directed path. With regard to intuitionistic fuzzy rough graphs, the objective of this work is to investig

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Meenakshi, A., S. Dhanushiya, Hong Qin, and Muniyandy Elangovan. "Optimal Network Analysis through Vertex Order Coloring of Intuitionistic Fuzzy Graph Operations." Journal of Mathematics 2024, no. 1 (2024). http://dx.doi.org/10.1155/2024/8898813.

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Intuitionistic fuzzy graphs (IFGs) are a powerful tool for modeling uncertainty and complex relationships. They offer versatile frameworks for addressing real‐world challenges. In this research, we have introduced intuitionistic fuzzy vertex order coloring (IFVOC) and analyzed the alpha‐strong (), beta‐strong (), and gamma‐strong () vertices through their degree. We explored important theorems based on the types of strong vertices, broadening the scope of our study. We analyzed multiple IFG products to determine the most optimal network based on some important metrics, including the weight and

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Gong, Zengtai, and Lele He. "Connectivity Status of Intuitionistic Fuzzy Graphs and Its Applications." International Journal of Foundations of Computer Science, October 19, 2023, 1–17. http://dx.doi.org/10.1142/s0129054123500223.

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The connectivity is one of the crucial parameters of network used to transport network flow, routing problems and bandwidth allocation problems. The increased connectivity makes a network more stable. In this paper, a new parameter called connectivity status of a vertex is introduced in the intuitionistic fuzzy graph. The related definitions and propositions of connectivity status of a vertex are proposed and investigated in an intuitionistic fuzzy graph. Specifically, connectivity status and status sequence are defined and analysed with various examples. After deleting a vertex, we classify t

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