On Vertex Identifying Codes For Infinite Lattices

Date
2011-01-01
Authors
Stanton, Brendon
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Mathematics
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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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Keywords
Density, Graph, Graph Theory, Identifying Code, Infinite Grid, Infinite Lattice
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