Bondage and Non-Bondage Number o Bondage and Non-Bondage Number of Anti-Fuzzy Graph

Bondage and Non-Bondage Number of Anti-Fuzzy Graph

Abstract

Many studies have focused on the development of fuzzy graph theory. Graph domination is a key area of study within fuzzy graph theory. It has been applied in numerous fields to address real-world issues such as multi-attribute, multi-object, multi-agent decision-making problems, neural networks, and other areas. This paper aims to define the 𝔟ondage and non-𝔟ondage sets of anti-fuzzy graphs and analyze the 𝔟ondage number and non-𝔟ondage number of anti-fuzzy graphs. The properties of the 𝔟ondage and non-𝔟ondage numbers of anti-fuzzy graphs are examined. Several examples are used to illustrate the 𝔟ondage and non-𝔟ondage numbers of anti-fuzzy graphs. Additionally, the bounds of 𝔟ondage and non-𝔟ondage numbers are discussed, and some theorems related to 𝔟ondage and non-𝔟ondage numbers are proven.