Independent domination in regular graphs

Let G be a simple graph of order n. The independent domination numberi(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. Motivated by work of Cockayne et al. (1991) and Cockayne and Mynhardt (1989), we investigate the maximum value of the product of the independent domination numbers of a graph and its complement, as a function of n. In particular we prove that if G is regular then i(G) · i(G) < (n + 14)2/12.68.