scholarly journals Liars Dominationset on fuzzy Graphs under Join, Corona, and Lexicographic Products

2019 ◽  
Vol 8 (2S3) ◽  
pp. 1608-1610
Keyword(s):  
Dominating Set ◽  
Fuzzy Graph ◽  
Fuzzy Graphs ◽  
The Given

A set L⊆ V (G) of a fuzzy graphG = (V, E) is a liar's dominating set if (1) for all υ∈ V (G), |N[υ] ∩ L | ≥ 2 and (2) for each pair ( u, v) ∈ V (G) of unmistakable vertices, |N[u] ∪ N[v] ∩ L| ≥ 3. In this paper, we consider the liar's control number of some center graphs. Crown result of twofuzzy graphs which is undifferentiated from the idea crown item activity in fresh graph hypothesis is characterized. The level of an edge in crown result of fuzzy graphs is acquired. Additionally, the level of an edge in fuzzy graph framed by this activity as far as the level of edges in the given fuzzy graphs in some specific cases is found. In addition, it is demonstrated that crown result of two fuzzy graphs is compelling when two fuzzy graphs are powerful fuzzy graphs

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 Certain Properties of Domination in Product Vague Graphs With an Application in Medicine

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaolong Shi ◽  
Saeed Kosari
Keyword(s):  
Graph Theory ◽  
Real World ◽  
Dominating Set ◽  
Independent Set ◽  
Fuzzy Graph ◽  
Medical Sciences ◽  
Total Dominating Set ◽  
Fuzzy Graphs ◽  
Vague Graph ◽  
Real World Problems

The product vague graph (PVG) is one of the most significant issues in fuzzy graph theory, which has many applications in the medical sciences today. The PVG can manage the uncertainty, connected to the unpredictable and unspecified data of all real-world problems, in which fuzzy graphs (FGs) will not conceivably ensue into generating adequate results. The limitations of previous definitions in FGs have led us to present new definitions in PVGs. Domination is one of the highly remarkable areas in fuzzy graph theory that have many applications in medical and computer sciences. Therefore, in this study, we introduce distinctive concepts and properties related to domination in product vague graphs such as the edge dominating set, total dominating set, perfect dominating set, global dominating set, and edge independent set, with some examples. Finally, we propose an implementation of the concept of a dominating set in medicine that is related to the COVID-19 pandemic.

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 A Survey on Domination in Vague Graphs with Application in Transferring Cancer Patients between Countries

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1258
Author(s):  
Yongsheng Rao ◽  
Ruxian Chen ◽  
Pu Wu ◽  
Huiqin Jiang ◽  
Saeed Kosari
Keyword(s):  
Dominating Set ◽  
Sufficient Conditions ◽  
Real Life ◽  
Practical Interest ◽  
Independent Set ◽  
Fuzzy Graph ◽  
Edge Dominating Set ◽  
Fuzzy Graphs ◽  
Wide Range ◽  
Dominance Set

Many problems of practical interest can be modeled and solved by using fuzzy graph (FG) algorithms. In general, fuzzy graph theory has a wide range of application in various fields. Since indeterminate information is an essential real-life problem and is often uncertain, modeling these problems based on FG is highly demanding for an expert. A vague graph (VG) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems in which fuzzy graphs may not succeed in bringing about satisfactory results. Domination in FGs theory is one of the most widely used concepts in various sciences, including psychology, computer sciences, nervous systems, artificial intelligence, decision-making theory, etc. Many research studies today are trying to find other applications for domination in their field of interest. Hence, in this paper, we introduce different kinds of domination sets, such as the edge dominating set (EDS), the total edge dominating set (TEDS), the global dominating set (GDS), and the restrained dominating set (RDS), in product vague graphs (PVGs) and try to represent the properties of each by giving some examples. The relation between independent edge sets (IESs) and edge covering sets (ECSs) are established. Moreover, we derive the necessary and sufficient conditions for an edge dominating set to be minimal and show when a dominance set can be a global dominance set. Finally, we try to explain the relationship between a restrained dominating set and a restrained independent set with an example. Today, we see that there are still diseases that can only be treated in certain countries because they require a long treatment period with special medical devices. One of these diseases is leukemia, which severely affects the immune system and the body’s defenses, making it impossible for the patient to continue living a normal life. Therefore, in this paper, using a dominating set, we try to categorize countries that are in a more favorable position in terms of medical facilities, so that we can transfer the patients to a suitable hospital in the countries better suited in terms of both cost and distance.

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 Complete Regular Fuzzy Graphs

2019 ◽  
Vol 8 (3S3) ◽  
pp. 25-29
Keyword(s):  
Fuzzy Graph ◽  
Induced Subgraph ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex ◽  
The Given ◽  
Regular Property

In this paper, some properties of complete degree and complete regular fuzzy graphs are discussed. They are illustrated through various examples. It is proved that every fuzzy graph is an induced subgraph of a complete regular fuzzy graph. The procedure described in the proof is illustrated through an example. Also the complete degree of a vertex in fuzzy graphsformed by the operation Union in terms of the complete degree of vertices in the given fuzzy graphs for some particular cases are obtained. Using them, their complete regular property is studied.

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