The Double Domination Number Of Fuzzy Graphs

International Journal of Computing Algorithm, 2013

A set D ⊂ V of a given fuzzy graph G(V,ρ,μ)is a dominating set if for every u∈V-Dthere exists v∈D such that (u,v) is a strong arc andρ(u)≤ρ(v) and if the number of vertices of D is minimum then it is called a minimum dominating set of G. Domination number of G is the sum of membership values of vertices ofa minimum dominating setD and it is denoted byγ(D). In this paper we study domination in fuzzy graphs. Also we formulate an algorithm to find dominating set for a given fuzzy graph.

IAEME Publications, 2019

In this paper we discuss about a dominating set, minimum dominating set and domination number in a fuzzy graph and an algorithm is also formulated for finding a dominating set of a fuzzy graph.

Far East Journal of Applied Mathematics, 2008

com . yahoo @ 70 Mahioub in . co . yahoo @ ndsoner Abstract:

2013

In this article we give a new definition of direct product of two arbitrary fuzzy graphs. We define the concepts of domination and total domination in this new product graph. We obtain an upper bound for the total domination number of the product fuzzy graph. Further we define the concept of total α-domination number and derive a lower bound for the total domination number of the product fuzzy graph in terms of the total α-domination number of the component graphs. A lower bound for the domination number of the same has also been found.

Research Square (Research Square), 2022

In this paper, we consider the notion of (crisp)domination set of fuzzy graphs via fuzzy bridges and compute domination numbers in this regard. Indeed it is tried to combine the fuzzy values of both vertices and edges to present this domination number in fuzzy graphs. The main method in this research is based on the computation of domination number of complete fuzzy graphs with vertices depend on the distinct fuzzy value and generalization of domination number of complete fuzzy graphs with vertices depending on the indistinct fuzzy value. As a result of this study is to compute of domination number of cyclic strong fuzzy graphs with vertices depending on the distinct fuzzy value. Also, it is analyzed some critical vertices in cyclic strong fuzzy graphs such that by linking some edges in these vertices to cyclic strong fuzzy graphs, the domination number of complete fuzzy graphs is obtained. Thus there is a relationship between the domination number of cyclic strong fuzzy graphs and the domination number of complete fuzzy graphs by removing some special edges in complete fuzzy graphs. The paper includes implications for the development of fuzzy graphs, and for modeling the uncertainty problems by domination numbers and applications in some complex networks. The new conception of domination number in fuzzy graphs based on fuzzy bridges was given for the first time in this paper. We find an Algorithm that can compute the domination number of complete and cyclic strong fuzzy graphs and can apply it in the modeling of real problems of complex networks.

The International journal of analytical and experimental analysis, 2020

A set D⊆V is called triple dominating set of a fuzzy graph G. If every vertex in V is dominated by at least three vertices in D. The minimum cardinality of fuzzy triple dominating set is called fuzzy triple domination number of G and is denoted by γ₃(G).The aim of this paper is to find on what relations the fuzzy graph has perfect triple domination number and independent triple domination number for a connected fuzzy is obtained .

THE 11TH NATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS

In this paper, we study various domination concepts like domination, 2-domination, edge domination, perfect edge domination, strong domination, split domination, perfect domination and double domination in double layered fuzzy graphs. We further investigate some of its properties.

International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 2005

In this paper we introduce the concepts of domination and total domination in product fuzzy graphs. We determine the domination number γ(G) and the total domination number γ t (G) for several classes of product fuzzy graphs and obtain bounds for the same. We also obtain Nordhaus -Gaddum type results for these parameters.

The fuzzy domination number (G) of the fuzzy graph G is the minimum cardinality taken over all fuzzy minimal dominating set of G. The minimum cardinality of a fuzzy k-dominating set is called the fuzzy k-dominating number k(G) .The maximum incident degree of a fuzzy graph is (G).In this paper we prove some theorems that relate the parameters(G),k(G),(G).

2029

In this paper we focus on 2-domination number of an intervalvalued fuzzy graphs G by using effective edge and is denoted by γ 2 (G) and obtain some results on γ 2 (G), the relationship between γ 2 (G) and some other, known parameters concepts are obtained. Finally the domatic number of interval-valued fuzzy graph is introduced further some results on this concept are investigated.