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 the set. Independent sets are important in various applications, such as scheduling problems and network theory, where it is essential to select non-overlapping elements. The size of the largest independent set in a graph is known as the independence number. Finding independent sets can be useful for optimizing resources, as it allows for the selection of elements that do not interfere with each other. This concept is widely studied in the field of combinatorics and has implications in computer science and operations research.