منابع مشابه
Semidefinite relaxation for dominating set
‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exp...
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Finding a dominating set of minimum cardinality is an NP-hard graph problem, even when the graph is bipartite. In this paper we are interested in solving the problem on graphs having a large independent set. Given a graph G with an independent set of size z, we show that the problem can be solved in time O∗(2n−z), where n is the number of vertices of G. As a consequence, our algorithm is able t...
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Many authors studied cooperative games that arise from variants of dominating set games on graphs. In wireless networks, the connected dominating set is used to reduce routing table size and communication cost. In this paper, we introduce a connected dominating set game to model the cost allocation problem arising from a connected dominating set on a given graph and study its core. In addition,...
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A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, Ars Comb. 89 (2008), 159–162) implies that every connected graph of minimum degree at least three has a dominating set D and a total dominating set T which are disjoint. We show that the Petersen graph is the only such graph for which D ∪ T necessarily contains all vertices of the graph.
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ژورنال
عنوان ژورنال: Journal of Nonlinear Sciences and Applications
سال: 2008
ISSN: 2008-1901
DOI: 10.22436/jnsa.001.01.02