Bounds for the ratio between the domination number and the independent domination number

Abstract

In this article we present new and improved results for the ratio between the independent domination number and the domination number in graphs with bounded degree. We present a general formula, that, for a fixed maximum degree, allows to compute an upper bound for this ratio as a function of an upper bound $β|V|$ for the independent domination number. We also apply this formula to several known upper bounds for the independent domination number. Furthermore we present constructions giving lower bounds for the best possible upper bound in various classes of graphs with bounded degree.