Properties of Regular Uniform k—Stratified Graphs

A regular graph G = (V, E) is a k-stratified graph if V is partitioned into V1, V2, …, Vk subsets called strata. The stratification splits the degree dv ∀v ϵ V into k-integers dv1, dv2, …, dvk each one corresponding to a stratum. If dv1 = dv2 = … = dvk ∀v ϵ V then G is called regular uniform k-stratified, RUks(n, d) where n is the cardinality of the vertex set in each stratum and d is the degree of every vertex in each stratum. For every k, the class RUks(n, d) has a unique graph generator class RUls(n, d) derived by decomposition of graphs in RUks(n, d). We investigate the minimization of the cardinality of V, the colorability, vertex coloring and the diameter of the graphs in the class. We also deal with complexity questions concerning RUks(n, d). Some well-known computer network models such as barrel shifters and hypercubes are shown to belong in RUks(n, d).