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.

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 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.

scholarly journals Perfect Dominating Set of An Interval-Valued Fuzzy Graphs

2021 ◽  
pp. 35-46
Author(s):  
Faisal M. AL-Ahmadi ◽  
Mahiuob M. Q. Shubatah
Keyword(s):  
Network Theory ◽  
Dominating Set ◽  
Domination Number ◽  
Fuzzy Graphs ◽  
Relationship Of ◽  
The Relationship ◽  
Interval Valued

Aims/ Objectives: Perfect domination is very much useful in network theory, Electrical stations and several fields of mathematics. In This paper, perfect domination in an intervalvalued fuzzy graphs is defined and studied. Some bounds on perfect domination number γp(G) are provided for several interval-valued fuzzy graphs, such as complete, wheel and star,.. etc. Furthermore, the relationship of γp(G): with some other known parameters in interval-valued fuzzy graphs investigated with some suitable examples.

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 The Results on Vertex Domination in Fuzzy Graphs

2018 ◽  
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, α-strong 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 γv 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 α-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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