Novel Concept of Interval-Valued Neutrosophic Incidence Graphs with Application

Abstract

Abstract: Neutrosophic set (NS) is a framework used when the imprecision and uncertainty of an event are described based on three possible aspects, i.e., the membership degree, neutral membership degree and non-membership degree. On the other hand, neutrosophic graphs (NG) are applicable to deal with bulk information events. Furthermore, the incidence graph concept in neutrosophic sets contains a handful of problems like decision-making as well as, social and communication networks. This paper aims to propose the interval-valued neutrosophic sets to incidence graph and represent a new concept, namely interval-valued neutrosophic incidence graph (IVNIG). An IVNIG is a generalization of the concept of single-valued neutrosophic incidence graph (SVNIG). Moreover, some properties related to IVNIG, such as strong edge, strong pair, strong cut pair and neutrosophic incidence cut pair, are also discussed using suitable examples. The defined new concept of IVNIG is applied and investigated on a practical problem of safe root travelling.

Keywords

• bridge
• cut pair
• interval-valued neutrosophic incidence graphs
• strong edge