Vulnerability Parameters in Neutrosophic Graphs

Abstract

Let 𝐺 = (U, V) be a Single valued Neutrosophic graph. A subset 𝑆 ∈ 𝑈(𝐺) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, |𝑠(𝑢)– 𝑠(𝑣)| ≤ 1, 𝑢, 𝑣 ∊ 𝑆. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as E𝐼(𝐺) = 𝑚𝑖𝑛{|𝑆| + 𝑚(𝐺 − 𝑆 ): 𝑆 is a score equitable set in 𝐺}, where 𝑚(𝐺 − 𝑆) denotes the order of the largest component in 𝐺 − 𝑆. The strong integrity of Single valued Neutrosophic graph G which is defined as S𝐼(𝐺) = 𝑚𝑖𝑛{|𝑆| + 𝑚(𝐺 −𝑆 ): 𝑆 is a strong score set in 𝐺}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds.

Keywords

• score equitable sets
• strong score equitable sets
• equitable integrity
• strong equitable integrity