On the Domination Number of Some Families of Special Graphs - Agustin, Ika Hesti; Dafik, Dafik (Prosiding Seminar Matematika dan Pendidikan Matematik, 2014)
A domination in graphs is part of graph theory which has many applications. Its application includes the morphological analysis, computer network communication, social network theory, CCTV installation, and many others. A set D of vertices of a simple graph G, that is a graph without loops and multiple edges, is called a dominating set if every vertex uin V(G)-D is adjacent to some vertex vin D. The domination number of a graphÂ G, denoted by gamma(G), is the order of a smallestÂ dominating set of G. A dominating set D with |D|=gamma(G) is called a minimum dominating set, see Haynes and Henning citeHay1 . This research aims to find the domination number of some families of special graphs, namely Spider Web graph Wb_n, Helmet graph H_n,m, Parachute graph Pc_n, and any regular graph. The results shows that the resulting domination numbers meet the lower bound of an obtained lower bound gamma(G) of any graphs.