A Characterization of Large (<em>t,r</em>)-Regular Graphs.

<p>A graph <em>G</em> is a (<em>t</em>,<em>r</em>)-regular graph if every collection of <em>t</em> independent vertices is collectively adjacent to exactly <em>r</em> vertices. In this thesis, we will present a complete characterization of (<em>t</em>,<em>r</em>)-regular graphs of order <em>n</em> if <em>n</em> is sufficiently large. Furthermore, we will show that all graphs of this type are isomorphic to <em>K_s</em> + <em>mK_p</em> where <em>t</em>(<em>p</em> - 1) + <em>s</em> = <em>r</em>.</p>

Name thesis:degree_name

MS (Master of Science)

Level thesis:degree_level

Thesis - restricted

Discipline thesis:degree_discipline

Mathematical Sciences

Grantor dc:publisher

East Tennessee State University

Year dc:date.issued

2000

Author dc:creator

• Gosnell, Shannon Leah

• graph theory
• regular
• (t r)-regular
• r-regular
• Mathematics
• Physical Sciences and Mathematics

Statement dc:rights

• Copyright by the authors.

Repository record dc:identifier

https://dc.etsu.edu/etd/7

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-1039