Generalized Fibonacci Cubes

Abstract

We present a new class of interconnection topolo gies called the generalized Fibonacci cubes (GFCs, for short) that encompass a range of networks such as the popular Boolean cube (hypercube) and the recent second-order Fibonacci cube in [5]. We show that each GFC has a recursive and self-similar structure and hence exhibits fault tolerant features. We also show that each GFC admits simple embedding of other useful net works such as cycles, trees, and meshes. The GFCs may find applications in fault-tolerant com puting.