The product of the independent domination numbers of a graph and its complement (Q1179268)

In an undirected, simple graph \(G\), let \(i(G)\) denote the smallest cardinality of a maximal independent set of vertices. The quantity \(i(G)\) is also known as the independent domination number of \(G\). The authors improve the best known upper bound for \(i(G)i(\bar G)\) from \(\lceil p(p+2)/4\rceil\) to \(\min\{(p+3)^ 2/8,(p+8)^ 2/10.8\}\), where \(p\) is the order of \(G\) and \(\bar G\) is the complement of \(G\).