The linear layout of the incomplete hypercube

In this paper, we study the linear layout problem of an incomplete hypercube by the embedding-in-book technique. An incomplete hypercube is a generalization of the hypercube in the sense that the number of nodes can be an arbitrary number. Embedding a graph in a book is to place nodes on the spine of a book and to draw the edges such that edges residing in a page do not cross. In this paper, we propose a scheme to embed an incomplete hypercube of 2/sup n/ + 2/sup m/ nodes, where n > m /spl ges/ 0, with n - 1 pages, cumulative page width 2/sup n/ + 2/sup m/ - 3; and book width 2/sup n - 1/ + 2/sup m - 1/ for n > m > 0, 2/sup n-1/ for n > m = 0. Moreover, this scheme can be applied to an arbitrary size of an incomplete hypercube.