On parameters related to strong and weak domination in graphs

Abstract

Let G be a graph. Then μ( G)⩽| V( G)|− δ( G) where μ( G) denotes the weak or independent weak domination number of G and μ( G)⩽| V( G)|− Δ( G) where μ( G) denotes the strong or independent strong domination number of G. We give necessary and sufficient conditions for equality to hold in each case and also describe specific classes of graphs for which equality holds. Finally, we show that the problems of computing i w and i st are NP-hard, even for bipartite graphs.