منابع مشابه
Identifying codes of cycles with odd orders
The problem of the r -identifying code of a cycle Cn has been solved totally when n is even. Recently, S. Gravier et al. give the r -identifying code for the cycle Cn with the minimum cardinality for odd n, when n ≥ 3r + 2 and gcd(2r + 1, n) 6= 1. In this paper, we deal with the r -identifying code of the cycle Cn for odd n, when n ≥ 3r + 2 and gcd(2r + 1, n) = 1. c © 2007 Elsevier Ltd. All rig...
متن کاملCycles with consecutive odd lengths
In this paper we prove that there exists an absolute constant c > 0 such that for every natural number k, every non-bipartite 2-connected graph with average degree at least ck contains k cycles with consecutive odd lengths. This implies the existence of the absolute constant d > 0 that every non-bipartite 2-connected graph with minimum degree at least dk contains cycles of all lengths modulo k,...
متن کاملIdentifying codes and locating-dominating sets on paths and cycles
Let 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} and Dr(x) = Nr[x] ∩ D, where d(x, y) denotes the number of edges in any shortest path between x and y. D is known as an r-identifying code (r-locating-dominating set, respectively), if for all vertices x ∈ V (x ∈ V \D, respectively), Dr(x) are all nonempty and different. In this paper, w...
متن کاملIdentifying and locating-dominating codes on chains and cycles
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 centered at v, i.e., the set of all vertices within distance r from v. If for all vertices v ∈ V (respectively, v ∈ V \C), the sets Br (v) ∩ C are all nonempty and different, then we call C an r -identifying code (respectively, an r -...
متن کاملGuessing Numbers of Odd Cycles
For a given number of colours, s, the guessing number of a graph is the base s logarithm of the size of the largest family of colourings of the vertex set of the graph such that the colour of each vertex can be determined from the colours of the vertices in its neighbourhood. An upper bound for the guessing number of the n-vertex cycle graph Cn is n/2. It is known that the guessing number equal...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2008
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2007.09.006