Improved book-embeddings of incomplete hypercubes
In this paper, we show that any incomplete hypercube with, at most, 2n+2n?1+2n?2 2 n + 2 n ? 1 + 2 n ? 2 vertices can be embedded in n?1 n ? 1 pages for all n?4 n ? 4 . For the case n?4 n ? 4 , this result improves Fang and Lais result that any incomplete hypercube with, at most, 2n+2n?1 2 n + 2 n ? 1 vertices can be embedded in n?1 n ? 1 pages for all n?2 n ? 2 . Besides this, we show that the result can be further improved when n n is large  e.g.,any incomplete hypercube with at most 2n+2n?1+2n?2+2n?7 2 n + 2 n ? 1 + 2 n ? 2 + 2 n ? 7 (respectively, 2n+2n?1+2n?2+2n?7+2n?230 2 n + 2 n ? 1 + 2 n ? 2 + 2 n ? 7 + 2 n ? 230 ) vertices can be embedded in n?1 n ? 1 pages for all n?9 n ? 9 (respectively, n?232 n ? 232 ).
book-embedding incomplete hypercube pagenumber interconnection networks