A bipolar model is a significant model wherein positive data revels the liked object, while negative data speaks the disliked object. The principle reason for analysing the vague graphs is to demonstrate the stability of few properties in a graph, characterized or to be characterized in using vagueness. In this present research article, the new concept of neutrosophic bipolar vague sets are initiated. Further, its application to neutrosophic bipolar vague graphs are introduced. Moreover, some remarkable properties of strong neutrosophic bipolar vague graphs, complete neutrosophic bipolar vague graphs and complement neutrosophic bipolar vague graphs are explored and the proposed ideas are outlined with an appropriate example.

Neutrosophic vague graphs are employed as a mathematical key to hold an imprecise and unspecified data. Vague sets gives more intuitive graphical notation of vague information, that delicates crucially better analysis in data relationships, incompleteness and similarity measures. In this paper, the neutrosophic bipolar vague line graphs are introduced. The necessary and sufficient condition for a line graph to be neutrosophic bipolar vague line graph is provided. Further, homomorphism, weak vertex and weak line isomorphism are discussed. The given results are illustrated with suitable example.

This manuscript is devoted to study a new concept of intuitionistic bipolar neutrosophic set with the operations like union, intersection and complement. Also, an application to intuitionistic bipolar neutrosophic graph with examples are developed. Further, we presented the Cartesian product, cross product, lexicographic product and strong product with suitable examples.

One of the important non-linear data structures in Computer Science is graph. Most of the real life network, be it a road transportation network, or airlines network or a communication network etc., cannot be exactly transformed into a graph model, but into a Multigraphs model. The Multigraph is a topological generalization of the graph where multiple links (or edges/arcs) mayexist between two nodes unlike in graph.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc

In this study, we re-define some operations on bipolar neutrosophic soft sets differently from the studies. On this operations are given interesting examples and them basic properties. In the direction of these newly defined operations, we construct the bipolar neutrosophic soft topological spaces. Finally, we introduce basic definitions and theorems on bipolar neutrosophic soft topological spaces.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles from this issue: Reduction of indeterminacy of gray-scale image in bipolar neutrosophic domain, Single Valued Neutrosophic Coloring, An Integrated Neutrosophic and MOORA for Selecting Machine Tool, Plithogenic Fuzzy Whole Hypersoft Set, Construction of Operators and their Application in Frequency Matrix Multi Attribute Decision Making Technique, Pi-Distance of Rough Neutrosophic Sets for Medical Diagnosis, Machine learning in Neutrosophic Environment: A Survey.