Affiliations: [a] Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan
| [b] Young Researchers and Elite club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Correspondence:
[*]
Corresponding author. Sumera Naz, Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore-54590, Pakistan. Tel.: +92 42 99231241; E-mail: [email protected].
Abstract: The concepts of graph theory are applied in many areas of computer science including image segmentation, data mining, clustering, image capturing and networking. Fuzzy graph theory is successfully used in many problems, to handle the uncertainty that occurs in graph theory. A single valued neutrosophic graph (SVNG) is an instance of a neutrosophic graph and a generalization of the fuzzy graph, intuitionistic fuzzy graph, and interval-valued intuitionistic fuzzy graph. In this paper, the basic operations on SVNGs such as direct product, Cartesian product, semi-strong product, strong product, lexicographic product, union, ring sum and join are defined. Moreover, the degree of a vertex in SVNGs formed by these operations in terms of the degree of vertices in the given SVNGs in some particular cases are determined. Finally, an application of single valued neutrosophic digraph (SVNDG) in traval time is provided.
Keywords: Neutrosophic graph, direct product, Cartesian product, semi-strong product, strong product, lexicographic product, degree of a vertex
