Independent domination in subcubic graphs of girth at least six

A set S of vertices in 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, i(G), of G is the minimum cardinality of an independent dominating set. In this paper, we extend the work of Henning, Löwenstein, and Rautenbach (2014) who proved that if G is a bipartite, cubic graph of order n and of girth at least 6, then i(G)≤[Formula presented]n. We show that the bipartite condition can be relaxed, and prove that if G is a cubic graph of order n and of girth at least 6, then i(G)≤[Formula presented]n.