Integrity and Domination Integrity in Neutrosophic Soft Graphs

Abstract

Vagueness and uncertainty are two distinct models are represented by Fuzzy sets and Soft sets. The
combination of Soft sets and simple graphs produces soft graphs which is also an interesting concept to deal
with uncertainty problems. Any communication network can be modeled as a graph whose nodes are the
processors (stations) and a communication link as an edge between corresponding nodes. The stability of a
communication network is a very important factor for the network designers to reconstruct the it after the
failure of certain stations or communication links. Two essential quantities in an analysis of the vulnerability of a
communication network are (1) the number of nodes that are not functioning and (2) the size of a maximum order of a
remaining sub network within which mutual communications can still occur. C. A. Barefoot, et. al. [13] introduced the
concept of integrity. The extension of such a vulnerability parameter is studied in fuzzy graphs. Since
neutrosophic soft graphs are the most generalized network structure where we can define and study the
importance of the vulnerability parameters is made in this manuscript. Also, we introduce the domination
integrity of neutrosophic soft graphs and explain with suitable examples. Few bounds are obtained