DOMINATING SET Meaning and
Definition
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A dominating set, in the context of graph theory, refers to a subset of vertices within a graph that has control or influence over the entire graph. It is a fundamental concept used to study and analyze graph structures and their properties.
More specifically, a dominating set is a set of vertices in a graph G such that every vertex either belongs to the set or is adjacent to at least one vertex in the set. In other words, each vertex in the graph is either directly included in the dominating set or is connected to at least one vertex in the set through an edge. The dominating set essentially "dominates" or covers the graph by having control over all the vertices.
The size of a dominating set is determined by the number of vertices it contains. A minimum dominating set refers to a dominating set of the smallest possible size within the graph. Finding the minimum dominating set is often a computationally challenging problem known as the dominating set problem or the minimum dominating set problem.
Domination sets have important applications in various areas, such as network design, facility location, and social network analysis. By identifying dominating sets, researchers can gain insights into the overall structure and properties of a graph, including its connectivity, resilience, and efficiency. Moreover, dominating sets play a crucial role in solving other graph-related problems, such as vertex cover, independent set, and connected dominating set.
Common Misspellings for DOMINATING SET
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Etymology of DOMINATING SET
The word "dominating set" has its etymology rooted in mathematics and computer science.
The term "dominating set" is derived from the concept of domination in graph theory. In graph theory, a dominating set is a subset of vertices in a graph, where every vertex that is not in the subset is adjacent to at least one vertex within the subset.
The word "dominating" is used to describe the action or state of dominance. In the context of graph theory, a dominating set dominates the entire graph because it has control or influence over every vertex that is not a part of the set.
The use of the word "set" is self-explanatory, referring to a collection or group of objects. In the case of a dominating set, it is a defined collection of vertices in a graph.
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