General Bounds for Identifying Codes in Some Infinite Regular Graphs
نویسندگان
چکیده
Consider a connected undirected graph G = (V,E) and a subset of vertices C. If for all vertices v ∈ V , the sets Br(v) ∩ C are all nonempty and pairwise distinct, where Br(v) denotes the set of all points within distance r from v, then we call C an r-identifying code. We give general lower and upper bounds on the best possible density of r-identifying codes in three infinite regular graphs.
منابع مشابه
Identifying Codes with Small Radius in Some Infinite Regular Graphs
Let G = (V,E) be a connected undirected graph and S a subset of vertices. If for all vertices v ∈ V , the sets Br(v) ∩ S are all nonempty and different, where Br(v) denotes the set of all points within distance r from v, then we call S an r-identifying code. We give constructive upper bounds on the best possible density of r-identifying codes in four infinite regular graphs, for small values of r.
متن کاملIdentifying Codes in Vertex-Transitive Graphs and Strongly Regular Graphs
We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2 ln(|V |) + 1 where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that re...
متن کاملIdentifying codes in vertex-transitive graphs
We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2 ln(|V |) + 1 where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that re...
متن کاملLower Bounds for Identifying Codes in some Infinite Grids
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 unique. On a finite graph, the density of a code is |C|/|V (G)|, which naturally extends to a definition of density in certain infinite graphs which are locally finite. We present new lower bounds for densities of codes for some s...
متن کاملOn nested completely regular codes and distance regular graphs
Infinite families of linear binary nested completely regular codes with covering radius ρ equal to 3 and 4 are constructed. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter D = 3 or 4 are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 8 شماره
صفحات -
تاریخ انتشار 2001