Nested (2,r)-Regular Graphs and Their Network Properties
Document Type
Conference Proceeding
Publication Date
1-1-2014
Description
A graph G is a (t, r)-regular graph if every collection of t independent vertices is collectively adjacent to exactly r vertices. Let p, s, and m be positive integers, where m ≥ 2 and let G be a (2,r)-regular graph. If 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 in a (2,r)-regular graph with a (2, r')-regular graph and joining the vertices of the peripheral cliques. We examine the network properties such as the average path length, clustering coefficient, and the spectrum of these nested graphs.
Citation Information
Brooks, Josh; Knisley, Debra; and Knisley, Jeff. 2014. Nested (2,r)-Regular Graphs and Their Network Properties. Journal of Combinatorial Mathematics and Combinatorial Computing. Vol.88 27-38. ISSN: 0835-3026