ABSTRACT

Dominating set S in the graph G is a subset of V(G) such that each vertex G that is not element S is connected and have distance as one to S. The minimum cardinality between dominating sets on graph G was called dominating number of graph G and denoted \gamma(G) . Dominating set D in the graph G is a subset of E(G) such that each edge G that is not element D is connected and have distance as one to D . The minimum cardinality between dominating sets on graph G was called dominating edge number of graph G and denoted \gamma(G)' . In this paper, we determined one distanced dominating number of edge on Sierpinski S(n,C_4)  by inserting m vertices on each edge smallest fractal graph C_4  for further we found relation and genmeral formula of dominating set obtained. Based on the relation and the general form obtained. The result showed that dominating number of edge on Sierpinski graph S(n,C_4)  have a general form \gamma(G)'  2^(2n-2) *(m+\ceilling ((m+4)/3)).

 

Keywords: Dominating Number, Graf Sierpinski, Edge, Vertex.