Independent dominating sets in regular graphs

Let G be a simple, regular graph of order n and degree δ. The independent domination numberi(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. We establish new upper bounds, as functions of n and δ, for the independent domination number of regular graphs with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n/6<\delta< (3-\sqrt{5})n/2$\end{document}. Our two main theorems complement recent results of Goddard et al. (Ann. Comb., 2011) for larger values of δ.