Domination in bipartite graphs
نویسندگان
چکیده
منابع مشابه
Domination in bipartite graphs
The domination number γ(G) of a (finite, undirected and simple) graph G = (V,E) is the minimum cardinality of a set D ⊆ V of vertices such that every vertex in V \ D has a neighbour in D. This parameter is one of the most well-studied in graph theory and the two volume monograph [9, 10] provides an impressive account of the research related to this concept. Fundamental results about the dominat...
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A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locatingdominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number λ(G). An LD-set S of a graph G is global if it is an LD-set of both G and its compleme...
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DOMINATING SET remains NP -complete even when instances are restricted to bipartite graphs, however, in this case VERTEX COVER is solvable in polynomial time. Consequences to VECTOR DOMINATING SET as a generalization of both are discussed.
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A dominating set S of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LDcodes and the cardinality of an LD-code is the location-domination number, λ(G). An LD-set S of a graph G is global if it is an LD-set for both G and its complem...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.12.051