Add to ORKGAbstract An r-identifying code on a graph G is a set C ⊂ V (G) such that for every vertex in V (G), the intersection of the radius-r closed neighborhood with C is nonempty and different. Here, we provide an overview on codes for the n-dimensional lattice, discussing the case of 1-identifying codes, constructing a sparse code for the 4-dimensional lattice as well as showing that for fixed n, the minimum density of an r-identifying code is Θ(1/r n−1 )
Abstract. An identifying code C is a subset of the vertices of the square grid Z 2 with the property...
AbstractFor a graph G and a set D⊆V(G), define Nr[x]={xi∈V(G):d(x,xi)≤r} (where d(x,y) is graph theo...
AbstractLet Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hammin...
AbstractLet G=(V, E) be an undirected graph and C a subset of vertices. If the sets Br(v)∩C, v∈V, ar...
AbstractConsider a connected undirected graph G=(V,E), a subset of vertices C⊆V, and an integer r≥1;...
AbstractLet G=(V,E) be a graph and let r≥1 be an integer. For a set D⊆V, define Nr[x]={y∈V:d(x,y)≤r}...
AbstractConsider a connected undirected graph G=(V,E), a subset of vertices C⊆V, and an integer r⩾1;...
AbstractLet G be a graph and B(u) be the set of u with all of its neighbors in G. A set S of vertice...
AbstractLet G=(V,E) be an undirected graph and C a subset of vertices. If the sets Br(v)∩C, v∈V (res...
AbstractA subset C of vertices in a connected graph G=(V,E) is called (r,⩽l)-identifying if for all ...
AbstractLet G be a finite undirected graph with vertex set V(G). If v∈V(G), let N[v] denote the clos...
We investigate the following problem : given an undirected graph G = (V; E) provided with a distance...
AbstractAssume that G=(V,E) is a simple undirected graph, and C is a nonempty subset of V. For every...
AbstractAn identifying code of a graph G is a dominating set C such that every vertex x of G is dist...
Given a graph G, an identifying code D ⊆ V (G) is a vertex set such that for any two distinct vertic...
Abstract. An identifying code C is a subset of the vertices of the square grid Z 2 with the property...
AbstractFor a graph G and a set D⊆V(G), define Nr[x]={xi∈V(G):d(x,xi)≤r} (where d(x,y) is graph theo...
AbstractLet Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hammin...
AbstractLet G=(V, E) be an undirected graph and C a subset of vertices. If the sets Br(v)∩C, v∈V, ar...
AbstractConsider a connected undirected graph G=(V,E), a subset of vertices C⊆V, and an integer r≥1;...
AbstractLet G=(V,E) be a graph and let r≥1 be an integer. For a set D⊆V, define Nr[x]={y∈V:d(x,y)≤r}...
AbstractConsider a connected undirected graph G=(V,E), a subset of vertices C⊆V, and an integer r⩾1;...
AbstractLet G be a graph and B(u) be the set of u with all of its neighbors in G. A set S of vertice...
AbstractLet G=(V,E) be an undirected graph and C a subset of vertices. If the sets Br(v)∩C, v∈V (res...
AbstractA subset C of vertices in a connected graph G=(V,E) is called (r,⩽l)-identifying if for all ...
AbstractLet G be a finite undirected graph with vertex set V(G). If v∈V(G), let N[v] denote the clos...
We investigate the following problem : given an undirected graph G = (V; E) provided with a distance...
AbstractAssume that G=(V,E) is a simple undirected graph, and C is a nonempty subset of V. For every...
AbstractAn identifying code of a graph G is a dominating set C such that every vertex x of G is dist...
Given a graph G, an identifying code D ⊆ V (G) is a vertex set such that for any two distinct vertic...
Abstract. An identifying code C is a subset of the vertices of the square grid Z 2 with the property...
AbstractFor a graph G and a set D⊆V(G), define Nr[x]={xi∈V(G):d(x,xi)≤r} (where d(x,y) is graph theo...
AbstractLet Fn be the binary n-cube, or binary Hamming space of dimension n, endowed with the Hammin...