Novel Concept of Interval-ValuedNeutrosophic Incidence Graphswith Application

Neutrosophic set (NS) is a framework used when the imprecision and uncertainty of an event aredescribed based on three possible aspects,i.e.,the membership degree, neutral membership degreeand non-membership degree. On the other hand, neutrosophic graphs (NG)areapplicable to deal with bulkinformation events. Furthermore, the incidence graphconceptin neutrosophic sets containsa handful ofproblems like decision-makingas well as, social and communication networks. This paperaimsto propose the interval-valuedneutrosophic sets to incidence graph and represent a new concept,namely interval-valuedneutrosophic incidence graph (IVNIG). An IVNIG is a generalization of the concept of single-valued neutrosophic incidence graph (SVNIG). Moreover, someproperties related to IVNIG,such as strong edge, strong pair, strong cutpairand neutrosophicincidence cut pair,are also discussedusingsuitable examples.The defined new concept of IVNIG isappliedand investigated ona practical problem of safe root travelling.