FUZZY GRAPH STRUCTURE OF FLOWER GRAPHS

2017 ◽  
Vol 96 (4) ◽  
pp. 213-220
Author(s):  
Purnima Harinath ◽  
S. Lavanya
Keyword(s):  
Graph Structure ◽  
Fuzzy Graph

New concepts of domination in fuzzy graph structures with application

2021 ◽  
pp. 1-13
Author(s):  
A.A. Talebi ◽  
G. Muhiuddin ◽  
S.H. Sadati ◽  
Hossein Rashmanlou
Keyword(s):  
Intelligent Systems ◽  
Dominating Set ◽  
Domination Number ◽  
Graph Structure ◽  
Multiple Relationships ◽  
Fuzzy Graph ◽  
Complex Problems ◽  
Graph Structures ◽  
Fuzzy Graphs ◽  
New Concepts

Fuzzy graphs have a prominent place in the mathematical modelling of the problems due to the simplicity of representing the relationships between topics. Gradually, with the development of science and in encountering with complex problems and the existence of multiple relationships between variables, the need to consider fuzzy graphs with multiple relationships was felt. With the introduction of the graph structures, there was better flexibility than the graph in dealing with problems. By combining a graph structure with a fuzzy graph, a fuzzy graph structure was introduced that increased the decision-making power of complex problems based on uncertainties. The previous definitions restrictions in fuzzy graphs have made us present new definitions in the fuzzy graph structure. The domination of fuzzy graphs has many applications in other sciences including computer science, intelligent systems, psychology, and medical sciences. Hence, in this paper, first we study the dominating set in a fuzzy graph structure from the perspective of the domination number of its fuzzy relationships. Likewise, we determine the domination in terms of neighborhood, degree, and capacity of vertices with some examples. Finally, applications of domination are introduced in fuzzy graph structure.

scholarly journals Certain Concepts inm-Polar Fuzzy Graph Structures

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Akram ◽  
Noura Alshehri ◽  
Rabia Akmal
Keyword(s):  
Fuzzy Sets ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Cut Vertex ◽  
Graph Structures

We apply the concept ofm-polar fuzzy sets to graph structures. We introduce certain concepts inm-polar fuzzy graph structures, including strongm-polar fuzzy graph structure,m-polar fuzzyDi-cycle,m-polar fuzzyDi-tree,m-polar fuzzyDi-cut vertex, andm-polar fuzzyDi-bridge, and we illustrate these concepts by several examples. We present the notions ofϕ-complement of anm-polar fuzzy graph structure and self-complementary, strong self-complementary, totally strong self-complementarym-polar fuzzy graph structures, and we investigate some of their properties.

scholarly journals Decision-Making Analysis Based on Fuzzy Graph Structures

2020 ◽  
Vol 2020 ◽  
pp. 1-30 ◽  
Author(s):  
Ali N. A. Koam ◽  
Muhammad Akram ◽  
Peide Liu
Keyword(s):  
Decision Making ◽  
General Procedure ◽  
Combinatorial Problems ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
The Road ◽  
Research Article ◽  
Graph Structures ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex

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 are introduced. Further, the proposed concepts are explained through several numerical examples. In particular, applications of the fuzzy graph structures in decision-making process, regarding detection of marine crimes and detection of the road crimes, are presented. Finally, the general procedure of these applications is described by an algorithm.

scholarly journals Vague Graph Structure with Application in Medical Diagnosis

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1582
Author(s):  
Saeed Kosari ◽  
Yongsheng Rao ◽  
Huiqin Jiang ◽  
Xinyue Liu ◽  
Pu Wu ◽  
...  
Keyword(s):  
Medical Diagnosis ◽  
Social Systems ◽  
Medical Science ◽  
Real Life ◽  
Image Clustering ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Vague Graph

Fuzzy graph models enjoy the ubiquity of being in natural and human-made structures, namely dynamic process in physical, biological and social systems. As a result of inconsistent and indeterminate information inherent in real-life problems which are often uncertain, it is highly difficult for an expert to model those problems based on a fuzzy graph (FG). Vague graph structure (VGS) can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. Likewise, VGSs are very useful tools for the study of different domains of computer science such as networking, capturing the image, clustering, and also other issues like bioscience, medical science, and traffic plan. The limitations of past definitions in fuzzy graphs have led us to present new definitions in VGSs. Operations are conveniently used in many combinatorial applications. In various situations, they present a suitable construction means; therefore, in this research, three new operations on VGSs, namely, maximal product, rejection, residue product were presented, and some results concerning their degrees and total degrees were introduced. Irregularity definitions have been of high significance in the network heterogeneity study, which have implications in networks found across biology, ecology and economy; so special concepts of irregular VGSs with several key properties were explained. Today one of the most important applications of decision making is in medical science for diagnosing the patient’s disease. Hence, we recommend an application of VGS in medical diagnosis.

scholarly journals Fuzzy Graph Structures with Application

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 63 ◽  
Author(s):  
Muzzamal Sitara ◽  
Muhammad Akram ◽  
Muhammad Yousaf Bhatti
Keyword(s):  
General Procedure ◽  
Controversial Issues ◽  
Total Degree ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Graph Structures ◽  
Degree Of A Vertex

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.

scholarly journals Domination of Bipolar Fuzzy Graphs in Various Settings

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Shu Gong ◽  
Gang Hua ◽  
Wei Gao
Keyword(s):  
Dominating Set ◽  
Graph Analysis ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Dominating Sets ◽  
Critical Position ◽  
Fuzzy Graphs ◽  
Control Set ◽  
Bipolar Fuzzy Sets ◽  
Bipolar Fuzzy Graphs

AbstractBipolar fuzzy sets are used to describe the positive and negative of the uncertainty of objects, and the bipolar fuzzy graphs are used to characterize the structural relationship between uncertain concepts in which the vertices and edges are assigned positive and negative membership function values to feature the opposite uncertainty elevation. The dominating set is the control set of vertices in the graph structure and it occupies a critical position in graph analysis. This paper mainly contributes to extending the concept of domination in the fuzzy graph to the bipolar frameworks and obtaining the related expanded concepts of a variety of bipolar fuzzy graphs. Meanwhile, the approaches to obtain the specific dominating sets are presented. Finally, a numeral example on city data in Yunnan Province is presented to explain the computing of domination in bipolar fuzzy graph in the specific application.

\phi-Complement of intuitionistic fuzzy graph structure

2017 ◽  
Vol 12 ◽  
pp. 241-250
Author(s):  
Vandana Bansal ◽  
P.K. Sharma
Keyword(s):  
Graph Structure ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy

scholarly journals Application of Bipolar Fuzzy Sets in Graph Structures

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Muhammad Akram ◽  
Rabia Akmal
Keyword(s):  
Computer Science ◽  
Fuzzy Sets ◽  
Computational Intelligence ◽  
Combinatorial Problems ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Cut Vertex ◽  
Graph Structures ◽  
Bipolar Fuzzy Sets

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS), strong bipolar fuzzy graph structure, bipolar fuzzyNi-cycle, bipolar fuzzyNi-tree, bipolar fuzzyNi-cut vertex, and bipolar fuzzyNi-bridge, and illustrate these notions by several examples. We studyϕ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.

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