New Trends in Mathematical Sciences An algorithm for finding complementary nil dominating set in a fuzzy graph (original) (raw)
Related papers
Complementary nil domination in fuzzy graphs
In this paper, the complementary nil dominating set and its numbers in a fuzzy graph are defined. The bounds on this number is obtained for some standard fuzzy graphs. Theorems related to the above concepts are derived. Relation between complementary nil domination number and domination numbers are also derived. In this paper only connected fuzzy graphs which are not complete are considered.
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.
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.
Complementary nil dominating set in intuitionistic fuzzy graph using effective edges
2018
In this paper, the complementary nil dominating set and its number in an intuitionistic fuzzy graph is defined. The bounds on this number is obtained for some standard intuitionistic fuzzy graphs. Theorems related to the above concepts are derived. Relation between complementary nil domination number and domination numbers are also derived. In this paper only intuitionistic fuzzy graphs without isolated vertices but not complete are considered. 2010 AMS Classification: 05C72, 03F55, 05C69
Complementary Nil G-Eccentric Domination in Fuzzy Graphs
Advances in Mathematics: Scientific Journal
A g-eccentric dominating set D ⊆ V of a fuzzy graph G = (ρ, φ) is said to be a complementary nil g-eccentric dominating set (CNGED-set) if V −D contains no g-eccentric dominating set of G = (ρ, φ). The least scalar cardinality taken over all CNGED-set of G is called the complementary nil g-eccentric domination number of G = (ρ, φ). In this article, bounds for complementary nil g-eccentric domination number for a few standard fuzzy graph are given and theorems related to CNGED-sets are discussed. The relation between complementary nil g-eccentric domination number and other well known parameters are analyzed.
Domination Number Based on Fuzzy Bridges in Fuzzy Graphs and Applications
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 Double Domination Number Of Fuzzy Graphs
Abstract A subset D of V in a fuzzy graph G = (µ, ) is a double dominating set of G if for each vertex in V is dominated by at least two vertices in D. The double domination number of a fuzzy graph G is the minimum fuzzy cardinality of a double dominating set D and is denoted by dd(G) . In this paper we initiate the study of double domination in fuzzy graphs and present bounds and some exact values for dd(G). Also relationship between dd(G) and other known domination parameters are explored.
Trends on dominations of fuzzy graphs and anti fuzzy graphs
ESSENCE OF MATHEMATICS IN ENGINEERING APPLICATIONS: EMEA-2020
After introducing and developing fuzzy graph theory, a lot of studies have been done in this field. The object of this paper is to demonstrate various Dominations such as Edge domination, Total domination, Strong (weak) domination, Regular domination, connected domination, Split (non-split) domination in fuzzy graphs with their importance and applications in real world. We explored about Inverse Dominations in Fuzzy graphs. Some results are derived to various dominations in Fuzzy graphs. Fuzzy graphs found an increasing number of applications in prevailing science where the information inherent in the system varies with different levels of precision. We prompt some applications in modeling traffic and transportation problems, telecommunications, job allocation and at ATM centers. The wide varieties of domination parameters are defined.
Inverse Dominating Set in Fuzzy Graphs
Proceedings of the Jangjeon …, 2008
Let G be a graph with p vertices and let D be a minimum dominating set of G. If V − D contains a dominating set D of G, then D is called an inverse dominating set of G with respect to D. The inverse domination number γ (G) of G is the cardinality of a smallest inverse dominating set of G. This concept was introduced and studied by Kulli and Domke in