The minimum identifying code graphs
نویسندگان
چکیده
منابع مشابه
Extremal graphs for the identifying code problem
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an identifying code of minimum possible size turned out to be a challenging problem. It was proved by N. Bertrand, I. Charon, O. Hudry and A. Lobstein that if a graph on n vertices with...
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The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...
متن کاملOn Minimum Identifying Codes in Some Cartesian Product Graphs
An identifying code in a graph is a dominating set that also has the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. The minimum cardinality of an identifying code, or ID code, in a graph G is called the ID code number of G and is denoted γ(G). In this paper, we give upper and lower bounds for the ID code number of the prism of a graph...
متن کاملNew Bounds on the Minimum Density of a Vertex Identifying Code for the Infinite Hexagonal Grid
For a graph, G, and a vertex v ∈ V (G), let N [v] be the set of vertices adjacent to and including v. A set D ⊆ V (G) is a vertex identifying code if for any two distinct vertices v1, v2 ∈ V (G), the vertex sets N [v1]∩D and N [v2]∩D are distinct and non-empty. We consider the minimum density of a vertex identifying code for the infinite hexagonal grid. In 2000, Cohen et al. constructed two cod...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2012
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.01.015