A note on connected bipartite graphs having independent domination number half their order Original Research Article

The independent domination number of a graph G, denoted by i(G), is the minimum cardinality of a maximal independent set of G. A maximal independent set of cardinality i(G) in G we call an i(G)-set. In this paper, we solve the following problem due to Rautenbach and Volkmann: characterization of the connected bipartite graphs G with i(G) = n/2, where n = |V(G)|. Furthermore, we provide a constructive characterization of tree T with i(T) = n/2, where n = |V(T)|.