Abstract
A vertex u in an undirected graph G = ( V, E ) is said to dominate all its adjacent vertices and itself. A subset D of V is a dominating set in G if every vertex in G is dominated by a vertex in D , and is a minimum dominating set in G if no other dominating set in G has fewer vertices than D . The domination number of G is the cardinality of a minimum dominating set in G . The problem of determining, for a given positive integer k and an undirected graph G , whether G has a dominating set D in G satisfying ¦ D ¦ ≤ k , is a well-known NP-complete problem. Cockayne have presented a linear time algorithm for finding a minimum dominating set in a tree. In this paper, we will present a linear time algorithm for finding a minimum dominating set in a series-parallel graph.
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