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 ð”Ÿondage and non-ð”Ÿondage sets of anti-fuzzy graphs and analyze the ð”Ÿondage number and non-ð”Ÿondage number of anti-fuzzy graphs. The properties of the ð”Ÿondage and non-ð”Ÿondage numbers of anti-fuzzy graphs are examined. Several examples are used to illustrate the ð”Ÿondage and non-ð”Ÿondage numbers of anti-fuzzy graphs. Additionally, the bounds of ð”Ÿondage and non-ð”Ÿondage numbers are discussed, and some theorems related to ð”Ÿondage and non-ð”Ÿondage numbers are proven.