On Vertex Identifying Codes For Infinite Lattices
Date
2011-01-01
Authors
Stanton, Brendon
Major Professor
Advisor
Ryan Martin
Committee Member
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Altmetrics
Abstract
For any position integer r, an r-identifying code on a graph G is a set C which is a subset of V(G) such that the intersection of the radius-r closed neighborhood with C is nonempty and pairwise distinct. For a finite graph, the density of a code is |C|/|V(G)|, which extends naturally to a definition of density on certain infinite graphs which are locally finite. This thesis explores the concept of density on certain infinite graphs, each of which have a representation on an n-dimensional lattice and finds some new bounds for these densities.
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Type
dissertation
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Sat Jan 01 00:00:00 UTC 2011