Abstract
A k-dominating set of a graph G=( V, E) is a set of vertices D such that for every vertex x in V there exists some vertex y in D satisfying d( x, y)≤ k. A k-dominating set D of G is connected if the subgraph G[ D] induced by D is connected and total if G[ D] has no isolated vertex. This paper presents efficient algorithms for finding a minimum cardinality k-dominating set without taking power, connected k-dominating set and total 1-dominating set of a sun-free chordal graph. NP-complete results for these problems are also discussed.
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