On the independent domination number of random regular graphs

A dominating set 9 of a graph G is a subset of V(G) such that, for every vertex v G V(G), either in nu is an element of D, or there exists a vertex u is an element of D, that is adjacent to nu. We are interested in finding dominating sets of small cardinality. A dominating set J of a graph G is said to be independent if no two vertices of J are connected by an edge of G. The size of a smallest independent dominating set of a graph G is the independent domination number of G. In this paper we present upper bounds on the independent domination number of random regular graphs. This is achieved by analysing the performance of a randomized greedy algorithm on random regular graphs using differential equations.