Independent domination in subcubic bipartite graphs of girth at least six

A set S of vertices of a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in  S. The independent domination number of G, denoted by  i(G), is the minimum cardinality of an independent dominating set of G. In this paper, we show that if G is a bipartite cubic graph of order  n and of girth at least  6, then i(G)≤4n/11.