منابع مشابه
Open neighborhood locating dominating sets
For a graph G that models a facility, various detection devices can be placed at the vertices so as to identify the location of an intruder such as a thief or saboteur. Here we introduce the open neighborhood locating-dominating set problem. We seek a minimum cardinality vertex set S with the property that for each vertex v its open neighborhood N(v) has a unique non-empty intersection with S. ...
متن کاملLocating-dominating sets in twin-free graphs
A locating-dominating set a of graph G is a dominating set D of G with the additional property that every two distinct vertices outside D have distinct neighbors in D; that is, for distinct vertices u and v outside D, N(u) ∩D 6= N(v) ∩D where N(u) denotes the open neighborhood of u. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. The location-dom...
متن کاملMetric-Locating-Dominating Sets in Graphs
If u and v are vertices of a graph, then d(u, v) denotes the distance from u to v. Let S = {v1, v2, . . . , vk} be a set of vertices in a connected graph G. For each v ∈ V (G), the k-vector cS(v) is defined by cS(v) = (d(v, v1), d(v, v2), · · · , d(v, vk)). A dominating set S = {v1, v2, . . . , vk} in a connected graph G is a metric-locatingdominating set, or an MLD-set, if the k-vectors cS(v) ...
متن کاملLocating and total dominating sets in trees
Locating and Total Dominating Sets in Trees by Jamie Marie Howard A set S of vertices in a graph G = (V,E) is a total dominating set of G if every vertex of V is adjacent to some vertex in S. In this thesis, we consider total dominating sets of minimum cardinality which have the additional property that distinct vertices of V are totally dominated by distinct subsets of the total dominating set.
متن کاملOptimal locating-total dominating sets in strips of height 3
A set C of vertices in a graph G = (V,E) is total dominating in G if all vertices of V are adjacent to a vertex of C. Furthermore, if a total dominating set C in G has the additional property that for any distinct vertices u, v ∈ V \ C the subsets formed by the vertices of C respectively adjacent to u and v are different, then we say that C is a locating-total dominating set in G. Previously, l...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2019
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2019.09.051