An independent set in graph theory is a collection of vertices in a graph, where no two vertices are adjacent. This means that there are no edges connecting any pair of vertices within this set. Independent sets are important in various applications, such as scheduling problems and network theory, where certain elements must be selected without conflicts. The size of the largest independent set in a graph is known as the independence number. Finding the maximum independent set is a common problem in computer science and mathematics, often requiring algorithms to explore different combinations of vertices. Understanding independent sets helps in optimizing resources and improving efficiency in various fields.