title: Some isomorphic properties ofm-polar fuzzy graphs with applications.
abstract: 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 handlem-polar fuzzy information by combining the theory ofm-polar fuzzy sets with graphs. We introduce the notion of weak self complementm-polar fuzzy graphs and establish a necessary condition form-polar fuzzy graph to be weak self complement. Some properties of self complement and weak self complementm-polar fuzzy graphs are discussed. The order, size, busy vertices and free vertices of anm-polar fuzzy graphs are also defined and proved that isomorphicm-polar fuzzy graphs have same order, size and degree. Also, we have presented some results of busy vertices in isomorphic and weak isomorphicm-polar fuzzy graphs. Finally, a relative study of complement and operations onm-polar fuzzy graphs have been made. Applications ofm-polar fuzzy graph are also given at the end.
authors.affiliation: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102 India.
authors.forename: Ganesh
authors.initials: G
authors.lastname: Ghorai
authors.affiliation: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102 India.
authors.forename: Madhumangal
authors.initials: M
authors.lastname: Pal
keywords: 5-Polar fuzzy evaluation graph; Busy and free vertices; Isomorphisms; Order and size; Self complement and weak self complement; m-Polar fuzzy graphs