Upper bound of Liar’s Domination number for fuzzy graphs and some specific fuzzy graphs

Let G = <σ,μ> be a fuzzy graph, on V which represents a building, computer network, computer system etc.., Each vertex represents location in the building, router in a computer network, or processor in a computer system. Each edge represents lines between locations, processors. Let x be an intruder and its possible locations are V(G). Let there exists only one intruder, D ⊆ V(G) is said to be liar's domination set in such a way that the intruder location could be identified when only one protection device of S is faulty. We assume that the protection devices located in S could identify & report the intruder location. In this paper we have given the upper boundof liar's domination number for specific fuzzy graphs and also some related theorems.