On Bondage Numbers of Graphs -- a survey with some comments

TL;DR

This survey reviews the current state of research on bondage numbers in graphs, discussing known results, open problems, conjectures, and related concepts in the field.

Contribution

It compiles and comments on existing results, problems, and conjectures about bondage numbers, providing a comprehensive overview and insights into future research directions.

Findings

Summarizes key known results on bondage numbers.

Highlights open problems and conjectures in the field.

Introduces and discusses other types of bondage numbers.

Abstract

The bondage number of a nonempty graph $G$ is the cardinality of a smallest edge set whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. This lecture gives a survey on the bondage number, including the known results, problems and conjectures. We also summarize other types of bondage numbers.