Range-Valued Fuzzy Colouring Of Intuitionistic Fuzzy Graphs With Application

Intuitionistic fuzzy graph, belonging to fuzzy graphs family has good capabilities when facing with problems that cannot be expressed by fuzzy graphs. Intuitionistic fuzzy graph can handle the vagueness connected with the incompatible and determinate information of any real-world problem, where fuzzy graphs may not succeed to bear satisfactory results. The previous restrictions in fuzzy graphs have led us to propose new definitions in intuitionistic fuzzy graphs. Colouring problem in graphs theory is one of the key issues that has many applications in computer science and social networks. Today, many researchers are trying to prove its application in medical sciences and psychology. Hence, in this paper, new concept of colouring of intuitionistic fuzzy graphs has been introduced. Also, some important terms like power cut graph of intuitionistic fuzzy graphs, range-valued fuzzy colour, chromatic number of an intuitionistic fuzzy graph colouring have been described. Some relevant results are proved. This technique is used to colour world political map mentioning the strength of relationship among the countries. Also, a new kind of traffic signal system has been proposed.