1. The algorithmic complexity of mixed domination in graphs
- Author
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Zhao, Yancai, Kang, Liying, and Sohn, Moo Young
- Subjects
- *
COMPUTER algorithms , *POLYNOMIALS , *SET theory , *DOMINATING set , *GRAPH theory , *COMPUTER science - Abstract
Abstract: Let be a simple graph with vertex set and edge set . A subset is a mixed dominating set if every element is either adjacent or incident to an element of . The mixed domination problem is to find a minimum mixed dominating set of . In this paper we first prove that a connected graph is a tree if and only if its total graph is strongly chordal, and thus we obtain a polynomial-time algorithm for this problem in trees. Further we design another linear-time labeling algorithm for this problem in trees. At the end of the paper, we show that the mixed domination problem is NP-complete even when restricted to split graphs, a subclass of chordal graphs. [Copyright &y& Elsevier]
- Published
- 2011
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