3,004 research outputs found
Improved Bounds for -Identifying Codes of the Hex Grid
For any positive integer , an -identifying code on a graph is a set
such that for every vertex in , the intersection of the
radius- closed neighborhood with is nonempty and pairwise distinct. For
a finite graph, the density of a code is , which naturally extends
to a definition of density in certain infinite graphs which are locally finite.
We find a code of density less than , which is sparser than the prior
best construction which has density approximately .Comment: 12p
Social interaction of cancer survivors in Malta : a sociological analysis
This research analyzes social interaction of cancer patients in Malta. In particular it applies a qualitative sociological approach to verify how cancer patients interact with family members and society. The research concludes that social interaction of cancer survivors in Malta is characterized by mixed experiences, but at the same time, all cancer patients emphasize the importance of family support. A major finding is that cancer patients do not simply receive support from family members, but also provide it themselves to their relatives. This is not an intended effect of cancer survivorship, but nevertheless it helps strengthen social bonds within families of cancer patients.peer-reviewe
On two variations of identifying codes
Identifying codes have been introduced in 1998 to model fault-detection in
multiprocessor systems. In this paper, we introduce two variations of
identifying codes: weak codes and light codes. They correspond to
fault-detection by successive rounds. We give exact bounds for those two
definitions for the family of cycles
Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets
An identifying code of a (di)graph is a dominating subset of the
vertices of such that all distinct vertices of have distinct
(in)neighbourhoods within . In this paper, we classify all finite digraphs
which only admit their whole vertex set in any identifying code. We also
classify all such infinite oriented graphs. Furthermore, by relating this
concept to a well known theorem of A. Bondy on set systems we classify the
extremal cases for this theorem
On the size of identifying codes in triangle-free graphs
In an undirected graph , a subset such that is a
dominating set of , and each vertex in is dominated by a distinct
subset of vertices from , is called an identifying code of . The concept
of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in
1998. For a given identifiable graph , let \M(G) be the minimum
cardinality of an identifying code in . In this paper, we show that for any
connected identifiable triangle-free graph on vertices having maximum
degree , \M(G)\le n-\tfrac{n}{\Delta+o(\Delta)}. This bound is
asymptotically tight up to constants due to various classes of graphs including
-ary trees, which are known to have their minimum identifying code
of size . We also provide improved bounds for
restricted subfamilies of triangle-free graphs, and conjecture that there
exists some constant such that the bound \M(G)\le n-\tfrac{n}{\Delta}+c
holds for any nontrivial connected identifiable graph
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