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 Some Results on Point Set Domination of Fuzzy Graphs

2013 ◽  
Vol 13 (2) ◽  
pp. 58-62
Author(s):  
S. Vimala ◽  
J. S. Sathya
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Fuzzy Graph ◽  
Minimal Point ◽  
Minimum Cardinality ◽  
Fuzzy Graphs ◽  
Point Set

Abstract Let G be a fuzzy graph. Let γ(G), γp(G) denote respectively the domination number, the point set domination number of a fuzzy graph. A dominating set D of a fuzzy graph is said to be a point set dominating set of a fuzzy graph if for every S⊆V-D there exists a node d∈D such that 〈S ∪ {d}〉 is a connected fuzzy graph. The minimum cardinality taken over all minimal point set dominating set is called a point set domination number of a fuzzy graph G and it is denoted by γp(G). In this paper we concentrate on the point set domination number of a fuzzy graph and obtain some bounds using the neighbourhood degree of fuzzy graphs.

On (r,s)-Fuzzy Domination in Fuzzy Graphs

2016 ◽  
Vol 12 (01) ◽  
pp. 1-10
Author(s):  
S. Arumugam ◽  
Kiran Bhutani ◽  
L. Sathikala
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Fuzzy Graph ◽  
Fuzzy Subset ◽  
Fuzzy Graphs ◽  
Finite Set

Let [Formula: see text] be a fuzzy graph on a finite set [Formula: see text] Let [Formula: see text] and [Formula: see text] A fuzzy subset [Formula: see text] of [Formula: see text] is called an [Formula: see text]-fuzzy dominating set ([Formula: see text]-FD set) of G if [Formula: see text] Then [Formula: see text] is called the [Formula: see text]-fuzzy domination number of [Formula: see text] where the minimum is taken over all [Formula: see text]-FD sets [Formula: see text] of [Formula: see text] In this paper we initiate a study of this parameter and other related concepts such as [Formula: see text]-fuzzy irredundance and [Formula: see text]-fuzzy independence. We obtain the [Formula: see text]-fuzzy domination chain which is analogous to the domination chain in crisp graphs.

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 A STUDY ON TRIPLE CONNECTED TOTAL PERFECT DOMINATION IN FUZZY GRAPHS

2020 ◽  
pp. 93-100
Author(s):  
K. ELAVARASAN ◽  
T. GUNASEKAR
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Fuzzy Graph ◽  
Fuzzy Graphs

In this paper, we introduce the concept of triple connected total perfect domination in fuzzy graph. We have defined and derived some results related to the triple connected total perfect domination number with examples. Finally the triple connected total perfect dominating set and number are obtained.

scholarly journals Nikfar Domination in Fuzzy Graphs

2019 ◽  
Author(s):  
Mohammadesmail Nikfar
Keyword(s):  
Transportation Planning ◽  
Dominating Set ◽  
Domination Number ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
Graph Property

We introduce a new variation on the domination theme which we call nikfar domination as reducing waste of time in transportation planning. We determine the nikfar domination number  v for several classes of fuzzy graphs. The bounds is obtained for it. We prove both of the Vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for nikfar domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. Finally, we discuss about nikfar dominating set of a fuzzy tree by using the bridges and -strong edges equivalence.

scholarly journals Vertex Domination in t-Norm Fuzzy Graphs

2018 ◽  
Author(s):  
Mohammadesmail Nikfar
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Fuzzy Graph ◽  
First Variation ◽  
Fuzzy Graphs ◽  
The First Variation ◽  
First Time ◽  
The Relationship

For the first time, We do fuzzification the concept of domination in crisp graph on a generalization of fuzzy graph by using membership values of vertices, α-strong edges and edges. In this paper, we introduce the first variation on the domination theme which we call vertex domination. We determine the vertex domination number γv for several classes of t-norm fuzzy graphs which include complete t-norm fuzzy graph, complete bipartite t-norm fuzzy graph, star t-norm fuzzy graph and empty t-norm fuzzy graph. The relationship between effective edges and α-strong edges is obtained. Finally, we discuss about vertex dominating set of a fuzzy tree with respect to a t-norm ⨂ by using the bridges and α-strong edges equivalence.

scholarly journals Vertex Domination in Fuzzy Graphs

2019 ◽  
Author(s):  
Mohammadesmail Nikfar
Keyword(s):  
Transportation Planning ◽  
Dominating Set ◽  
Domination Number ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
Graph Property ◽  
The Relationship

We introduce a new variation on the domination theme which we call vertex domination as reducing waste of time in transportation planning and optimization of transport routes. We determine the vertex domination number $\gamma_v$ for several classes of fuzzy graphs. The bounds is obtained for it. In fuzzy graphs, monotone decreasing property and monotone increasing property are introduced. We prove both of the vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for vertex domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. The relationship between several classes of operations on fuzzy graphs with the vertex domination number of them is studied. Finally, we discuss about vertex dominating set of a fuzzy tree by using the bridges and $\alpha$-strong edges equivalence.

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.

scholarly journals Wiener Index of Fuzzy Graph by Using Strong Domination

2021 ◽  
pp. 13-24
Author(s):  
Saqr H. AL- Emrany ◽  
Mahiuob M. Q. Shubatah
Keyword(s):  
Domination Number ◽  
Wiener Index ◽  
New Method ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
The Relationship

Aims/ Objectives: This paper presents a new method to calculate the Wiener index of a fuzzy graph by using strong domination number s of a fuzzy graph G. This method is more useful than other methods because it saves time and eorts and doesn't require more calculations, if the edges number is very larg (n). The Wiener index of some standard fuzzy graphs are investigated. At last, we nd the relationship between strong domination number s and the average (G) of a fuzzy graph G was studied with suitable examples.

scholarly journals The Results on Vertex Domination in Fuzzy Graphs

2019 ◽  
Author(s):  
Mohammadesmail Nikfar
Keyword(s):  
Domination Number ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
Graph Property ◽  
The Relationship

We do fuzzification the concept of domination in crisp graph by using membership values of nodes, $\alpha$-strong arcs and arcs. In this paper, we introduce a new variation on the domination theme which we call vertex domination. We determine the vertex domination number $\gamma_v$ for several classes of fuzzy graphs, specially complete fuzzy graph and complete bipartite fuzzy graphs. The bounds is obtained for the vertex domination number of fuzzy graphs. Also the relationship between $M$-strong arcs and $\alpha$-strong is obtained. In fuzzy graphs, monotone decreasing property and monotone increasing property is introduced. We prove the vizing's conjecture is monotone decreasing fuzzy graph property for vertex domination. we prove also the Grarier-Khelladi's conjecture is monotone decreasing fuzzy graph property for it. We obtain Nordhaus-Gaddum (NG) type results for these parameters. The relationship between several classes of operations on fuzzy graphs with the vertex domination number of them is studied.

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