Zero Sets in Graphs.

<p>Let <em>S</em> &#8838; <em>V</em> be an arbitrary subset of vertices of a graph <em>G</em> = (<em>V</em>,<em>E</em>). The differential &#8706;(<em>S</em>) equals the difference between the cardinality of the set of vertices not in <em>S</em> but adjacent to vertices in <em>S</em>, and the cardinality of the set <em>S</em>. The <em>differential of a graph G</em> equals the maximum differential of any subset <em>S</em> of <em>V</em> . A set <em>S</em> is called a <em>zero set</em> if &#8706;(<em>S</em>) = 0. In this thesis we introduce the study of zero sets in graphs. We give proofs of the existence of zero sets in various kinds of graphs such as even order graphs, bipartite graphs, and graphs of maximum degree 3. We also give proofs regarding the existence of graphs which contain no zero sets and the construction of zero-free graphs from graphs which contain zero sets.</p>

Name thesis:degree_name

MS (Master of Science)

Level thesis:degree_level

Thesis - restricted

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.issued

2010

Author dc:creator

• Scott, Hamilton

• Graph Theory
• Differentials
• Discrete Mathematics and Combinatorics
• Mathematics
• Physical Sciences and Mathematics

Statement dc:rights

• Copyright by the authors.

Repository record dc:identifier

https://dc.etsu.edu/etd/1705

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-3060