Nested (2,r)-regular graphs and their network properties.

<p>A graph <i>G</i> is a (<i>t</i>, <i>r</i>)-regular graph if every collection of <i>t</i> independent vertices is collectively adjacent to exactly <i>r</i> vertices. If a graph <i>G</i> is (2, <i>r</i>)-regular where <i>p</i>, <i>s</i>, and <i>m</i> are positive integers, and <i>m</i> &#8805; 2, then when <i>n</i> is sufficiently large, then <i>G</i> is isomorphic to <i>G = K_s+mK_p</i>, where 2(<i>p</i>-1)+<i>s</i> = <i>r</i>. A nested (2,<i>r</i>)-regular graph is constructed by replacing selected cliques with a (2,<i>r</i>)-regular graph and joining the vertices of the peripheral cliques. For example, in a nested '<i>s</i>' graph when <i>n = s + mp</i>, we obtain <i>n = s₁+m₁p₁+mp</i>. The nested '<i>s</i>' graph is now of the form <i>G_s = K_s1+m₁K_p1+mK_p</i>. We examine the network properties such as the average path length, clustering coefficient, and the spectrum of these nested graphs.</p>

Name thesis:degree_name

MS (Master of Science)

Level thesis:degree_level

Thesis - unrestricted

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.issued

2012

Author dc:creator

• Brooks, Josh Daniel

• Laplacian matrix
• clustering coefficient
• average path length
• graph theory
• 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/1471

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-2664