Fuzzy colouring of m -polar fuzzy graph and its application

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Abstract
In this article, a new idea of fuzzy coloring of m -polar fuzzy graph is presented while establishing the relationship between chromatic number of m -polar fuzzy graph and it’s underlying crisp graph. Some properties of m -polar fuzzy graph and new concepts of independently strong edge and independently weak edge in m -polar fuzzy graph are proved. The differences between fuzzy coloring of fuzzy graph and m -polar fuzzy graph are discussed. It is also shown that a m -polar fuzzy graph can be decomposed into m fuzzy graphs. Again, from m isomorphic fuzzy graph one can construct a m -polar fuzzy graph. A relation among chromatic numbers of m -polar fuzzy graph and m such graphs is established. Lastly a real life application of the fuzzy coloring is discussed.

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