A book consists of a line in the 3-dimensional space, called the spine, and a number of pages, each a half-plane with the spine as boundary. A book embedding (p, r) of a graph consists of a linear ordering of p, of vertices, called the spine ordering, along the spine of a book and an assignment r, of edges to pages so that edges assigned to the same page can be drawn on that page without crossing. That is, we cannot find vertices u, v, x, y with p(u) < p(x) < p(v) < p(y), yet the edges uv and xy are assigned to the same page, that is r(uv) = r(xy). The book thickness or page number of a graph G is the minimum number of pages in required to embed G in a book. In this paper we consider the Sun Graph or the Trampoline graph and obtain the printing cycle for embedding the Sun Graph in a single page. We also give a linear time algorithm for such an embedding.

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 5)

Pages:

31-36

Citation:

M. Banukumar "Embedding Sun Graphs in a Single Page", The Bulletin of Society for Mathematical Services and Standards, Vol. 5, pp. 31-36, 2013

Online since:

Mar 2013

Authors:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

Bernhart, F. and Kainen, P.C., The book thickness of a graph. J. Combin. Theory Ser. B. v27. 320-331.

T. C. Biedl, T. Shermer, S. Wiitesided, S. Wismath, Bounds for orthogonal 3-D graph drawing, Journal of Graph Algorithms Appl. 3(1999) 63-79.

F. R. K. Chung , Frank Thomson Leighton , Arnold L. Rosenberg, Embedding graphs in books: a layout problem with applications to VLSI design, SIAM Journal on Algebraic and Discrete Methods, v. 8 n. 1, pp.33-58, January 2, (1987).

F. R. K. Chung, F. T. Leighton, and A. L. Rosenbert, Diogenes - A methodology for designing fault-tolerant processor arrays, 13th International Conference of Fault- Tolerant Computing, 1983, pp.26-32.

Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, Introduction to Algorithms, PHI, Second Edition, (2005).

Hasunuma, T., Embedding iterated line digraphs in books. Networks. v40. 51-62.

Hasunuma, T., Yukio Shibata, Embedding de-Bruijn, Kautz and shuffle-exchange networks in books, Discrete Applied Mathematics, v. 78 n. 1-3, pp.103-116, Oct. 21, (1997).

Jywe-Fei Fang , Kuan-Chou Lai, Embedding the incomplete hypercube in books, Information Processing Letters, v. 96 n. 1, pp.1-6, 16 October (2005).

Konoe, M., Hagihara, K. and Tokura, N., On the pagenumber of hypercubes and cubeconnected cycles. IEICE Trans. vJ71-D. 490-500.

Muder, D.J., Weaver, M.L. and West, D.B., Pagenumber of complete bipartite graphs, Journal of Graph Theory. v12. 469-489.

L. Rosenbert, The Diogenes approach to testable fault-tolerant arrays into processors, IEEE Trans. Comput., C-32 (1983), 902-910.