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 (G). The set Sₖ (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 Sₖ (G). The minimum cardinality of a k-distance domination set in graph G is called the k-distance domination number and is denoted as ₖ (G). This paper investigated the 2-distance and 3-distance domination sets in the Sierpinski Star graph SSₙ and derived the number of 2-distance domination of ₂ (SSₙ) =1 for n3 and ₂ (SSₙ) =3. 3^ (n-3) for n3, as well as the 3-distance domination number of ₃ (SSₙ) =1 for n3 and ₃ (SSₙ) =3^ (n-3) for n3.