scholarly journals New Kinds of Global Domination In Fuzzy Graph Using Strong Arc – New Approach

2021 ◽  
Vol 23 (11) ◽  
pp. 655-670
Author(s):  
G.K. Malathi ◽  
◽  
C.Y. Ponnappan ◽  
Keyword(s):  
Domination Number ◽  
Fuzzy Graph ◽  
New Approach ◽  
Global Domination Number

In this paper we establish the relation between strong arc domination number and global domination number ( new approach ) of some standard graphs using strong arcs. Also various new kinds of global domination number of using strong arc is discussed.

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 On the upper geodetic global domination number of a graph

2020 ◽  
Vol 39 (6) ◽  
pp. 1627-1647
Author(s):  
X. Lenin Xaviour ◽  
S. Robinson Chellathurai
Keyword(s):  
Shortest Path ◽  
Connected Graph ◽  
Dominating Set ◽  
Domination Number ◽  
Proper Subset ◽  
Maximum Cardinality ◽  
General Properties ◽  
Geodetic Set ◽  
Positive Integers ◽  
Global Domination Number

A set S of vertices in a connected graph G = (V, E) is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A set D of vertices in G is called a dominating set of G if every vertex not in D has at least one neighbor in D. A set D is called a global dominating set in G if S is a dominating set of both G and Ḡ. A set S is called a geodetic global dominating set of G if S is both geodetic and global dominating set of G. A geodetic global dominating set S in G is called a minimal geodetic global dominating set if no proper subset of S is itself a geodetic global dominating set in G. The maximum cardinality of a minimal geodetic global dominating set in G is the upper geodetic global domination number Ῡg+(G) of G. In this paper, the upper geodetic global domination number of certain connected graphs are determined and some of the general properties are studied. It is proved that for all positive integers a, b, p where 3 ≤ a ≤ b < p, there exists a connected graph G such that Ῡg(G) = a, Ῡg+(G) = b and |V (G)| = p.

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 Detour global domination number of some graphs

2020 ◽  
Vol S (1) ◽  
pp. 552-555
Author(s):  
C. Jayasekaran ◽  
S.V. Ashwin Prakash
Keyword(s):  
Domination Number ◽  
Global Domination Number

A new approach for determining fuzzy chromatic number of fuzzy graph

2015 ◽  
Vol 28 (5) ◽  
pp. 2331-2341 ◽  
Author(s):  
Isnaini Rosyida ◽  
Widodo ◽  
Ch. Rini Indrati ◽  
Kiki A. Sugeng
Keyword(s):  
Chromatic Number ◽  
Fuzzy Graph ◽  
New Approach
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