The document discusses domination in fuzzy graphs, defining a dominating set and a minimum dominating set. It introduces the concept of the domination number, which is the sum of membership values of vertices in a minimum dominating set. Additionally, the paper presents an algorithm to find a dominating set for a given fuzzy graph.

1. International Journal of Computing Algorithm, Vol 2(2), December 2013
ISSN(Print):2278-2397
Website: www.ijcoa.com
On Domination in Fuzzy Graphs
D.Antony Xavior1
, D.Florence Isido1
, V.M.Chtira2
1
Department of Mathematics, Loyola College, Chennai
2
SKR Engineering College,Poonamalee,Chennai
E-mail: chithu1234@yahoo.com
Abstract
A set D ⊂ V of a given fuzzy graph G(V, ρ,μ) is a dominating set if for every u ∈ V −
D there exists v ∈ D such that (u, v) is a strong arc and ρ(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 of a minimum dominating set D
and it is denoted by γ(D). In this paper we study domination in fuzzy graphs. Also we
formulate an algorithm to find dominating set for a given fuzzy graph.