ON FUZZY CHROMATIC NUMBER OF CARTESIAN PRODUCT OF SOME FUZZY GRAPHS AND ITS APPLICATION
Given two fuzzy graphs and with crisp vertex sets and fuzzy edge sets Given a cartesian product Following the previous work in [17], we construct a fuzzy chromatic number of where the underlying graphs of and are path or complete graphs. We also investigate whether a property in crisp graphs is satisfied in cartesian product of fuzzy graphs or not. We verify this property through a defuzzification of fuzzy chromatic number depended on a decision level a for An application of the fuzzy chromatic number in a telecommunication network is also proposed. Theoretical results in this paper can contribute to a decision making model of network problems.
fuzzy graph, fuzzy chromatic number, cartesian product, defuzzification, telecommunication network.