4 research outputs found
Uncoverings on graphs and network reliability
We propose a network protocol similar to the -tree protocol of Itai and
Rodeh [{\em Inform.\ and Comput.}\ {\bf 79} (1988), 43--59]. To do this, we
define an {\em -uncovering-by-bases} for a connected graph to be a
collection of spanning trees for such that any -subset of
edges of is disjoint from at least one tree in , where is
some integer strictly less than the edge connectivity of . We construct
examples of these for some infinite families of graphs. Many of these infinite
families utilise factorisations or decompositions of graphs. In every case the
size of the uncovering-by-bases is no larger than the number of edges in the
graph and we conjecture that this may be true in general.Comment: 12 pages, 5 figure
Error-Correcting codes fromk-resolving sets
We demonstrate a construction of error-correcting codes from graphs by
means of k-resolving sets, and present a decoding algorithm which makes use
of covering designs. Along the way, we determine the k-metric dimension of
grid graphs (i.e., Cartesian products of paths)