Affiliations: [a] Department of Mathematics, National Institute of Technology, Durgapur, India
| [b] Department of Computer Science and Engineering, Saroj Mohan Institute of Technology, Hooghly, India
| [c] Department of Mathematics, National Institute of Technology, Durgapur, India
| [d] Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam | [e] Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam | [f] VNU Information Technology Institute, Vietnam National University, Hanoi, Vietnam
Abstract: Information in many real life problems collect from multi agents, i.e., "multipolar information" exists. This multipolar information cannot be properly modeled by m- polar fuzzy graph or intutionistic fuzzy graph. An m-polar neutrosophic model is very much efficient for such real word problems which can construct more precise, flexible, and comparable system as compared to the classical, fuzzy and neutrosophic graph models. In this paper, we present the definition of m-polar neutrosophic graph model. Some new operations, such as union, join, composition and ring sum of two m-polar neutrosophic graph are defined here. We define six new products on m-polar neutrosophic graphs namely strong product, semi strong product, complete product, direct product, cartesian product and lexicographic product. Some idea of complement, isomorphism, weak and co weak isomorphism on m-polar neutrosophic graph are introduced here. We also present several associated properties and theorems of m-polar neutrosophic graph. We introduce a model of m-polar neutrosophic graph, which is applied in evaluating the teacher’s performance of a college. The performances of the teachers are computed based on the response score (feedback) of the students of the college. We also present a numerical example to illustrate our proposed model.
