Independent domination in triangle-free graphs

Abstract

Let G be a simple graph of order n and minimum degree δ . The independent domination number 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 / 2 , for the independent domination number of triangle-free graphs, and over part of the range achieve best possible results.