The term "dominating set" refers to a subset of vertices in a graph that can control or influence the behavior of the entire graph. Some synonyms for this term might include: controlling set, influential set, powerful set, or ruling set. These words all suggest a group of vertices that have a significant impact on the structure and dynamics of the graph, and can be used interchangeably with "dominating set" in many contexts. Other related terms might include "center set," "core set," or "nucleus," which also refer to subsets of vertices that are critical to the graph's overall behavior and function.