Locating-Dominating Sets and Identifying Codes in Graphs of Girth at least 5
نویسندگان
چکیده
Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the dominating set. In this paper, we study the size of a smallest locating-dominating set or identifying code for graphs of girth at least 5 and of given minimum degree. We use the technique of vertexdisjoint paths to provide upper bounds on the minimum size of such sets, and construct graphs who come close to meet these bounds.
منابع مشابه
k-TUPLE DOMATIC IN GRAPHS
For every positive integer k, a set S of vertices in a graph G = (V;E) is a k- tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum cardinality of a k-tuple dominating set of G is the k-tuple domination number of G. When k = 1, a k-tuple domination number is the well-studied domination...
متن کاملEfficient Enumeration of Dominating Sets for Sparse Graphs
Dominating sets are fundamental graph structures. However, enumeration of dominating sets has not received much attention. This study aims to propose two efficient enumeration algorithms for sparse graphs. The first algorithm enumerates all the dominating sets for k-degenerate graphs in O (k) time per solution using O (n + m) space. Since planar graphs have a constant degeneracy, this algorithm...
متن کاملStrength of strongest dominating sets in fuzzy graphs
A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...
متن کاملExtremal cardinalities for identifying and locating-dominating codes in graphs
Consider a connected undirected graph G = (V ,E), a subset of vertices C ⊆ V , and an integer r 1; for any vertex v ∈ V , let Br(v) denote the ball of radius r centred at v, i.e., the set of all vertices linked to v by a path of at most r edges. If for all vertices v ∈ V (respectively, v ∈ V \C), the setsBr(v)∩C are all nonempty and different, then we call C an r-identifying code (respectively,...
متن کاملDecision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes
An identifying code is a subset of vertices of a graph with the property that each vertex is uniquely determined (identified) by its nonempty neighbourhood within the identifying code. When only vertices out of the code are asked to be identified, we get the related concept of a locating-dominating set. These notions are closely related to a number of similar and well-studied concepts such as t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 22 شماره
صفحات -
تاریخ انتشار 2015