Metric-locating-dominating sets of graphs for constructing related subsets of vertices
نویسندگان
چکیده
منابع مشابه
Metric-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 کاملNew results on metric-locating-dominating sets of graphs
A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distances from the elements of S, and the minimum cardinality of such a set is called the metric-locationdomination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominating sets to other special sets: ...
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 کاملVertices in all minimum paired-dominating sets of block graphs
Let G = (V,E) be a simple graph without isolated vertices. A set S ⊆ V is a paired-dominating set if every vertex in V − S has at least one neighbor in S and the subgraph induced by S contains a perfect matching. In this paper, we present a linear-time algorithm to determine whether a given vertex in a block graph is contained in all its minimum paired-dominating sets.
متن کاملLocating-Total Dominating Sets in Twin-Free Graphs: a Conjecture
A total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A locating-total dominating set of G is a total 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2018
ISSN: 0096-3003
DOI: 10.1016/j.amc.2018.03.053