Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
8-2012
Committee Chair or Co-Chairs
Debra J. Knisley
Committee Members
Robert A. Beeler, Arial Cintron-Aries
Abstract
A graph G is a (t, r)-regular graph if every collection of t independent vertices is collectively adjacent to exactly r vertices. If a graph G is (2, r)-regular where p, s, and m are positive integers, and m ≥ 2, then when n is sufficiently large, then G is isomorphic to G = Ks+mKp, where 2(p-1)+s = r. A nested (2,r)-regular graph is constructed by replacing selected cliques with a (2,r)-regular graph and joining the vertices of the peripheral cliques. For example, in a nested 's' graph when n = s + mp, we obtain n = s1+m1p1+mp. The nested 's' graph is now of the form Gs = Ks1+m1Kp1+mKp. We examine the network properties such as the average path length, clustering coefficient, and the spectrum of these nested graphs.
Document Type
Thesis - unrestricted
Recommended Citation
Brooks, Josh Daniel, "Nested (2,r)-regular graphs and their network properties." (2012). Electronic Theses and Dissertations. Paper 1471. https://dc.etsu.edu/etd/1471
Copyright
Copyright by the authors.