Abstract: A set D ⊆ V of vertices in a graph G = (V, E) is called a dominating set if every vertex v ∈ V (G) is either an element of D or is adjacent to an element of D [4].The domination number γ(G) is the minimum cardinality of the dominating set of G. This article embarks on an exploration of the domination number of a graph G. Additionally, it delves into the precise determination of minimum dominating set for certain well-known graphs. 2010 Mathematics Subject Classification: 059C.

Keywords: Dominating set, Domination number.