title: On m-polar fuzzy graph structures.
abstract: Sometimes information in a network model is based on multi-agent, multi-attribute, multi-object, multi-polar information or uncertainty rather than a single bit. An m-polar fuzzy model is useful for such network models which gives more and more precision, flexibility, and comparability to the system as compared to the classical, fuzzy and bipolar fuzzy models. In this research article, we introduce the notion of m-polar fuzzy graph structure and present various operations, including Cartesian product, strong product, cross product, lexicographic product, composition, union and join of m-polar fuzzy graph structures. We illustrate these operations by several examples. We also investigate some of their related properties.
authors.affiliation: Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan.
authors.forename: Muhammad
authors.initials: M
authors.lastname: Akram
authors.affiliation: Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan.
authors.forename: Rabia
authors.initials: R
authors.lastname: Akmal
authors.affiliation: Department of Mathematics, Faculty of Science, Al-Faisaliah Campus, King Abdulaziz University, Jeddah, Saudi Arabia.
authors.forename: Noura
authors.initials: N
authors.lastname: Alshehri
keywords: Cartesian product; Composition; Cross product; Join; Lexicographic product; Strong product; Union of two m-PFGSs; m-Polar fuzzy graph structure (m-PFGSs)