Graph theory is an highly use full tool in solving the combinatorial problem different areas including geometry, algebra, number theory, topology, operations research, optimization and computer science. The fuzzy systems have been used with success in last few years, in problems that involving the approximate reasoning. The research are in different disciplines including medical and life science, management sciences, social sciences, engineering, statistics, graph theory, artificial intelligence, data base, information systems and security, signal processing, multiagent systems and pervasive computing, pattern recognition, robotics, computer networks, expert systems, decision making, automata theory, etc.