Operations On Single Valued Neutrosophic Graphs With Application
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Operations on single valued neutrosophic graphs with application
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.
Operations on Single-Valued Neutrosophic Graphs
The concept of neutrosophic sets can be utilized as a mathematical tool to deal with imprecise and unspecified information. In this paper, we apply the concept of single-valued neutrosophic sets to graphs. We introduce the notion of single-valued neutrosophic graphs, and present some fundamental operations on single-valued neutrosophic graphs. We explore some interesting properties of single-valued neutrosophic graphs by level graphs. We highlight some flaws in the definitions of Broumi et al. [10] and Shah-Hussain [18]. We also present an application of single-valued neutrosophic graphs in social network.
Operations of Single Valued Neutrosophic Coloring
Smarandache introduced the concept of Neutrosophic which deals with membership, non-membership and indeterminacy values. Wang discussed the Single Valued Neutrosophic sets in 2010. Single Valued Neutrosophic graph was introduced by Broumi and in 2019 Single Valued Neutrosophic coloring was introduced. In this paper, some properties of the Single Valued Neutrosophic Coloring of Strong Single Valued Neutrosophic graph, Complete Single Valued Neutrosophic graph and Complement of Single Valued Neutrosophic graphs are discussed.