Independent domination in triangle-free graphs

Let G be a simple graph of order n   and minimum degree δδ. The independent domination number  i(G)i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. We establish upper bounds, as functions of n   and δ⩽n/2δ⩽n/2, for the independent domination number of triangle-free graphs, and over part of the range achieve best possible results.