{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T11:59:36Z","timestamp":1710244776344},"reference-count":8,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":6653,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems & Computers in Japan"],"published-print":{"date-parts":[[1989,1]]},"abstract":"Abstract<\/jats:title>By the book embedding of a graph is meant a procedure to place the vertices of a graph along the spine of a book and to draw the edges in several pages, where the edges in a page should not cross each other. By the page\u2010number of a graph is meant the minimum number of pages needed in the book embedding. This paper discusses the page\u2010numbers of the d<\/jats:italic>\u2010dimensional hypercube (CUBEd<\/jats:italic><\/jats:sub>) and the d<\/jats:italic>\u2010dimensional cube\u2010connected cycles (CCCd, h<\/jats:italic><\/jats:sub>) with length h<\/jats:italic>, which are considered as interesting as the processor network configuration for the parallel computer. It is already known that the upper and lower bounds of the page\u2010number of CUBEd<\/jats:italic><\/jats:sub>(d<\/jats:italic>\u22651) are d<\/jats:italic> and d<\/jats:italic>\/4, respectively. This paper shows that the page\u2010number of CUBEd<\/jats:italic><\/jats:sub> is exactly max{d<\/jats:italic>\u20101, 1}, and the upper bound of the page\u2010number of CCCd,h<\/jats:italic><\/jats:sub> (h<\/jats:italic>\u22653, h<\/jats:italic>\u2265d<\/jats:italic>\u22651) is max{d<\/jats:italic> \u2010 1, 1}. The page\u2010number of the graph can be utilized in the evaluation of the practical realizability of the processor network graph on WSI. In other words, the result in this paper can be used as an evaluation measure for the circuit scale, when the processor network with hypercube or cube\u2010connected cycles topology is to be realized on WSI.<\/jats:p>","DOI":"10.1002\/scj.4690200404","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T17:37:28Z","timestamp":1183829848000},"page":"34-47","source":"Crossref","is-referenced-by-count":1,"title":["Page\u2010number of hypercubes and cube\u2010connected cycles"],"prefix":"10.1002","volume":"20","author":[{"given":"Michiko","family":"Konoe","sequence":"first","affiliation":[]},{"given":"Ken'Ichi","family":"Hagihara","sequence":"additional","affiliation":[]},{"given":"Nobuki","family":"Tokura","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"F. R. K.Chung T.Leighton andA.Rosenberg.DIOGENES\u2014A methodology for designing fault\u2010tolerant processor arrays. The 13th International Conference on Fault\u2010Tolerant Computing pp.26\u201332(1983)."},{"key":"e_1_2_1_3_2","first-page":"175","volume-title":"Graph Theory and Its Applications to Algorithms and Computer Science","author":"Chung F. R. K.","year":"1985"},{"key":"e_1_2_1_4_2","volume-title":"Graph Theory","author":"Harary F.","year":"1971"},{"key":"e_1_2_1_5_2","first-page":"119","article-title":"Parallel computer launched off with hope and fear","volume":"407","author":"Inaba N.","year":"1986","journal-title":"Nikkei Elect."},{"key":"e_1_2_1_6_2","article-title":"The book\u2010embedding of the hypercube and the cube\u2010connected cycles","volume":"87","author":"Konoe M.","year":"1987","journal-title":"Tech. Rep. I.E.C.E., Japan"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1145\/358645.358660"},{"key":"e_1_2_1_8_2","first-page":"227","volume-title":"Aegean Architectures, Loutraki, Greece, Lecture Notes in Computer Science","author":"Rosenberg A.","year":"1986"},{"key":"e_1_2_1_9_2","first-page":"226","article-title":"Linear and Book Embeddings of Graphs","volume":"24","author":"Yannakakis M.","journal-title":"Commun. ACM"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690200404","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690200404","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T13:17:45Z","timestamp":1697980665000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690200404"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,1]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1989,1]]}},"alternative-id":["10.1002\/scj.4690200404"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690200404","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,1]]}}}