THE SPLIT 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.

The resolution of this article is to discuss the importance of Anti Fuzzy Graphs. The intense exertions of scientists are perceivable in the applicable creation of the theme participating understandable practicality and certainty. Fuzzy logic is announced to study the ambiguity of the incident by assigning a system of membership principles to the elements of the universal set ranging from 0 to 1. In this article we familiarized the thought of Split and Non-Split Domination on Anti Fuzzy Graph. Dominating sets have a vital function regarding the scheme of fuzzy graphs. A dominating set S of an Anti-fuzzy graph be a "Split dominating set" whether encouraged Anti fuzzy sub graph H = (, ,) is detached. The minimum fuzzy cardinality of a split dominating set of Anti fuzzy graph is signified by () We explored about Strong domination and weak domination in Anti fuzzy graphs and total dominations in Anti fuzzy graphs. Some results are derived to various dominations in Anti fuzzy graphs. Fuzzy graphs initiate an increasing amount of submissions in existing science wherever the evidence central in the system diverges with dissimilar stages of correctness.

Journal of Discrete Mathematical Sciences and Cryptography, 2009

A dominating set D of a graph G is a split dominating set if the induced subgraph < V − D > is disconnected. The split domination number γ s (G) is the minimum cardinality of a split dominating set. The concept of split domination number was introduced by Kulli and Janakiram. In this paper, some results on split domination are obtained.

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 .

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.

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.

Annals of Pure and Applied Mathematics, 2017

In this paper the concept of split domination and non-split domination in bipolar fuzzy graphs are introduced and investigated some of their properties. Also relationship between connected domination, split domination, strong split domination and non-split domination number in bipolar fuzzy graphs are discussed.

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.

Pan-American Journal of Mathematics

Let G = (p, q) be a connected graph and Me(G) be its corresponding edge semi-middle graph. A dominating set D ⊆ V [Me(G)] is split dominating set V [Me(G)] – D is disconnected. The minimum size of D is called the split domination number of Me(G) and is denoted by γs[Me(G)]. In this paper we obtain several results on split domination number.

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.