Graphical Analysis of Covering and Paired Domination in the Environment of Neutrosophic Information

Sami Ullah Khan,Zhen-Hua Ma,Naeem Jan,Abdul Nasir,G Muhiuddin

doi:10.1155/2021/5518295

Sami Ullah Khan, Zhen-Hua Ma + Show 3 more

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https://doi.org/10.1155/2021/5518295

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Abstract

Neutrosophic graph (NG) is a powerful tool in graph theory, which is capable of modeling many real-life problems with uncertainty due to unclear, varying, and indeterminate information. Meanwhile, the fuzzy graphs (FGs) and intuitionistic fuzzy graphs (IFGs) may not handle these problems as efficiently as NGs. It is difficult to model uncertainty due to imprecise information and vagueness in real-world scenarios. Many real-life optimization problems are modeled and solved using the well-known fuzzy graph theory. The concepts of covering, matching, and paired domination play a major role in theoretical and applied neutrosophic environments of graph theory. Henceforth, the current study covers this void by introducing the notions of covering, matching, and paired domination in single-valued neutrosophic graph (SVNG) using the strong edges. Also, many attention-grabbing properties of these concepts are studied. Moreover, the strong covering number, strong matching number, and the strong paired domination number of complete SVNG, complete single-valued neutrosophic cycle (SVNC), and complete bipartite SVNG are worked out along with their fascinating properties.

Highlights

Graph theory is one of the major branches of mathematics and combinatorics
One of the generalizations of fuzzy graphs (FGs) is intuitionistic fuzzy graph (IFG). e notion of intuitionistic fuzzy graphs (IFGs) was presented by Shannon and Atanassov who developed the idea of intuitionistic fuzzy sets (IFSs) relation, which was used in defining the IFGs [22]
Ey discussed the many properties, theorems, and proofs regarding IFSs and IFGs. e work of Atanassov and Shannon was extended by many researchers who presented its properties, types, and applications; for example, join, union, and product of two IFGs were defined by Parvathi et al, and strong products, direct products, and lexicographic products of two IFGs were presented by Rashmanlou et al e concepts of strong IFGs and intuitionistic fuzzy hypergraphs along with their applications were discussed by Akram and Davvaz [23, 24]

Summary

Introduction

Graph theory is one of the major branches of mathematics and combinatorics. It has many applications in numerous fields such as computer science, networking, geometry, algebra, set theory, economics, medicine, engineering, and chemistry. 3. Covering and Matching in Single-Valued Neutrosophic Graphs is section presents the definitions and examples of strong covering of vertices and edges, strong independent sets (SIS), and strong matchings (SM) using strong edges (SEs).

Results

Conclusion