INDEPENDENT SET Meaning and
Definition
-
An independent set, in the context of graph theory, refers to a subset of vertices within a graph that are not adjacent to each other. More precisely, in an undirected graph, an independent set is a collection of vertices in which no two vertices within the set are connected by an edge.
Formally, let G = (V, E) be an undirected graph, where V represents the set of vertices and E represents the set of edges. An independent set I within G is a subset of V, such that for any two vertices u and v in I, there is no edge (u, v) in E connecting them.
The concept of independent sets is used to identify and study patterns and structures within graphs. It plays a crucial role in various applications, including scheduling, resource allocation, and optimization problems. Finding the maximum independent set in a given graph is a well-known NP-hard problem, meaning it is computationally difficult to solve for large graphs.
The size of an independent set refers to the number of vertices it contains. The maximum independent set is the largest independent set present in a graph, while the minimum independent set is the smallest one. The independent domination number of a graph corresponds to the size of the maximum independent set. Furthermore, an independent set that covers all vertices in a graph is considered as a dominating set.
Common Misspellings for INDEPENDENT SET
- undependent set
- jndependent set
- kndependent set
- ondependent set
- 9ndependent set
- 8ndependent set
- ibdependent set
- imdependent set
- ijdependent set
- ihdependent set
- insependent set
- inxependent set
- incependent set
- infependent set
- inrependent set
- ineependent set
- indwpendent set
- indspendent set
- inddpendent set
- indrpendent set
Etymology of INDEPENDENT SET
The etymology of the term "independent set" can be understood by breaking down the two words it consists of.
1. Independent: This word originates from the Latin word "independens", which is formed by combining "in-" (meaning "not" or "without") and "dependens" (present participle of "dependere", meaning "to hang down" or "to depend"). "Independent" signifies something that is not dependent on or influenced by other things.
2. Set: The term "set" has its roots in Old English and Germanic languages. It can be traced back to the Proto-Germanic word "satjan", which means "to place" or "to set". In mathematics, a set is a collection of distinct objects with clear boundaries.
Infographic
Add the infographic to your website:
