Some isomorphic properties of -polar fuzzy graphs with applications.

The theory of graphs are very useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we present a frame work to handle -polar fuzzy information by combining the theory of -polar fuzzy sets with graphs. We introduce the notion of weak self complement -polar fuzzy graphs and establish a necessary condition for -polar fuzzy graph to be weak self complement. Some properties of self complement and weak self complement -polar fuzzy graphs are discussed. The order, size, busy vertices and free vertices of an -polar fuzzy graphs are also defined and proved that isomorphic -polar fuzzy graphs have same order, size and degree. Also, we have presented some results of busy vertices in isomorphic and weak isomorphic -polar fuzzy graphs. Finally, a relative study of complement and operations on -polar fuzzy graphs have been made. Applications of -polar fuzzy graph are also given at the end.