Uniform central graph and variations of hypercubes

An interest area of graph theory, especially in the telecommunications industry, is the study of centers of graphs. In particular, we would like to study so called Uniform Central Graph (UCG). A graph G is called UCG if the eccentric sets of all central vertices are the same (Choi and Manickam 1988). The traditional construction method of UCG has been based on the cartesian product of the UCG; the result is a new UCG with d(G) > 32 r(G). Moreover, the graphs constructed by this method is very large.;The objective of this investigation is the construction of UCG with any given diameters and radius that satisfies 2 ≤ r < d ≤ 2r. We found that given any graph G we can construct an UCG H having G as its center for any given 2 ≤ r(H) < d(H ) < 2r(H). In addition, we study to construction UCG from the Hypercubes or Boolean Cube, and from the subgraphs of hypercube, such as Fibonacci Cube (Wen-jing, H 1993), and the Lucas Cube (Murani, et al 2001) with d ≤ 32 r. (Abstract shortened by UMI.).