Question

Question: A dominating set of vertices in a simple graph is a set of vertices such that every other vertex is adjacent to at least one vertex of this set. A dominating set with the least number of vertices is called a minimum dominating set.Find a minimum dominating set for the given graph.

Short answer

.The minimum dominating set for the graph is.

Step-by-step solution

Concept/Significance of a dominating set

According to the graph theory, a dominating set for a graph is a subset of its vertices in which every vertex is adjacent to the set. The dominance number for the graph is the set of vertices within the dominant set.

Determination of the dominating set in the graph

Every vertex in the graph,a, b, c, and d, is adjacent to Vertex e, which satisfies the definition of a minimum dominating set.