Graph embedding aspect of IEH graphs

Abstract

In order to overcome the drawback of the hypercube that the number of nodes is limited to a power of two, the incrementally extensible hypercube (IEH) graph is derived for an arbitrary number of nodes [12]. In this paper, we first prove that the incomplete hypercube (IH) is a spanning subgraph of IEH. Next. we present a new method to construct an IEH From an IH. From the aspect of graph embedding, we determine the minimum size of the IEH that contains a complete binary tree. WI: then embed a torus (with a side length as power of two) into an IEH with dilation 1 and expansion 1.