2-Distance and 3-Distance Domination Numbers of the Sierpinski Star Graph

The domination set D(G) in graph G=(V(G),E(G)) is a subset of the vertex set in graph G such that every vertex in V(G)(G) is adjacent to at least one vertex in D(G). The minimum cardinality of a domination set in graph G is called the domination number and is denoted as γ(G). The set S_k (G) is called the k-distance domination set in graph G if every vertex v in V(G)_k (G) has a distance of less than or equal to k from at least one vertex in S_k (G). The minimum cardinality of a k-distance domination set in graph G is called the k-distance domination number and is denoted as γ_k (G). This paper investigated the 2-distance and 3-distance domination sets in the Sierpinski Star graph SS_n and derived the number of 2-distance domination of γ_2 (SS_n)=1 for n<3 and γ_2 (SS_n)=3.3^(n-3) for n≥3, as well as the 3-distance domination number of γ_3 (SS_n)=1 for n<3 and γ_3 (SS_n)=3^(n-3) for n≥3.