2-Domination Number of Butterfly Graphs

A new family of graphs called Butterfly Graphs is introduced recently and study of its parameters is under progress. Butterfly Graphs are undirected graphs and are widely used in interconnection networks. In this paper, we find 2-dominating sets of Butterfly graph and show that 2-domination number of $BF(n)$ is

$\gamma_{×2}(BF(n)) = 2^n$  if $n = 2$

$\gamma_{×2}(BF(n)) = k \times 2^n + r \times 2^{n-1}$  if $n = 3k + r.$