Ekinci, Gulnaz BoruzanliBujtas, Csilla2020-12-012020-12-0120202391-54552391-5455https://doi.org/10.1515/math-2020-0047https://hdl.handle.net/11454/62034Let k be a positive integer and let G be a graph with vertex set V(G). A subset D subset of V(G) is a k-dominating set if every vertex outside D is adjacent to at least k vertices in D. the k-domination number gamma(k)(G) is the minimum cardinality of a k-dominating set in G. For any graph G, we know that gamma(k)(G) >= gamma(G) + k - 2 where Delta(G) >= k >= 2 and this bound is sharp for every k >= 2. in this paper, we characterize bipartite graphs satisfying the equality for k >= 3 and present a necessary and sufficient condition for a bipartite graph to satisfy the equality hereditarily when k = 3. We also prove that the problem of deciding whether a graph satisfies the given equality is NP-hard in general.en10.1515/math-2020-0047info:eu-repo/semantics/openAccessdomination numberk-domination numberhereditary propertyvertex-edge coverTC-numbercomputational complexityArticle18873885WOS:0005642629000012-s2.0-85094137195Q3Q3