On Vertex Identifying Codes For Infinite Lattices

Thumbnail Image
Date
2011-01-01
Authors
Stanton, Brendon
Major Professor
Advisor
Ryan Martin
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Organizational Unit
Mathematics
Welcome to the exciting world of mathematics at Iowa State University. From cracking codes to modeling the spread of diseases, our program offers something for everyone. With a wide range of courses and research opportunities, you will have the chance to delve deep into the world of mathematics and discover your own unique talents and interests. Whether you dream of working for a top tech company, teaching at a prestigious university, or pursuing cutting-edge research, join us and discover the limitless potential of mathematics at Iowa State University!
Journal Issue
Is Version Of
Versions
Series
Department
Mathematics
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.

Comments
Description
Keywords
Citation
Source
Subject Categories
Copyright
Sat Jan 01 00:00:00 UTC 2011