Locating domination in bipartite graphs and their complements
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 set D of vertices in a graph G = (V, E) is a locating-dominating set (LDS) if for every two vertices u, v of V − D the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. The locating-domination number γL(G) is the minimum cardinality of a LDS of G, and the upper locating-domination number, ΓL(G) is the maximum cardinality of a minimal LDS of G. We present different bounds on ΓL(G) and γL...
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A locating-total dominating set of a graph G = (V (G), E(G)) with no isolated vertex is a set S ⊆ V (G) such that every vertex of V (G) is adjacent to a vertex of S and for every pair of distinct vertices u and v in V (G) − S, N(u) ∩ S = N(v) ∩ S. Let γ t (G) be the minimum cardinality of a locating-total dominating set of G. A graph G is said to be locating-total domination vertex critical if ...
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A locating-total dominating set (LTDS) S of a graph G is a total dominating set S of G such that for every two vertices u and v in V(G) − S, N(u)∩S ≠ N(v)∩S. The locating-total domination number ( ) l t G is the minimum cardinality of a LTDS of G. A LTDS of cardinality ( ) l t G we call a ( ) l t G -set. In this paper, we determine the locating-total domination number for the special clas...
متن کاملOn global location-domination in bipartite graphs
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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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2019
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.09.034