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Graph theory has applications in many areas of the computing, social and natural science. The theory is also intimately related to many branches of mathematics, including matrix theory, numerical analysis, probability, topology and combinatory. The fact is that graph theory serves as a mathematical for any system involving a binary relation. Over the last 50 year graph theory has evolved into an important mathematical tool in the solution of a wide variety of problems in many areas of society. A graph labeling is an assignment of integers to the vertices or edges or both, subject to certain conditions have been motivated by practical problems, labeled graphs serve useful mathematical models for a broad range of applications such as: coding theory, including the design of good types codes, synch-set codes, missile guidance codes and convolutional codes with optimal auto correlation properties. They facilitates the optimal nonstandard encodings of integer’s, labeled graph have also been applied in determining ambiguities in x-ray crystallographic analysis to design a communication network addressing system, data base management in determining optimal circuit layouts and radio astronomy problems etc.