{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:39Z","timestamp":1760242359068,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T00:00:00Z","timestamp":1495756800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The balanced hypercube network, which is a novel interconnection network for parallel computation and data processing, is a newly-invented variant of the hypercube. The particular feature of the balanced hypercube is that each processor has its own backup processor and they are connected to the same neighbors. A Hamiltonian bipartite graph with bipartition\n\t\n\t\tV\n\t\t0\n\t\n\t\u222a\n\t\n\t\tV\n\t\t1\n\t\n\tx\n\t\u2208\n\t\n\t\tV\n\t\t0\n\t\n\ty\n\t\u2208\n\t\n\t\tV\n\t\t1\n\t\n. It is known that each edge is on a Hamiltonian cycle of the balanced hypercube. In this paper, we prove that, for an arbitrary edge\n\te\nin the balanced hypercube, there exists a Hamiltonian path between any two vertices\n\tx\nand\n\ty\nin different partite sets passing through\n\te\nwith\n\te\n\t\u2260\n\tx\n\ty\n. This result improves some known results.<\/jats:p>","DOI":"10.3390\/sym9060079","type":"journal-article","created":{"date-parts":[[2017,5,30]],"date-time":"2017-05-30T04:35:42Z","timestamp":1496118942000},"page":"79","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Path Embeddings with Prescribed Edge in the Balanced Hypercube Network"],"prefix":"10.3390","volume":"9","author":[{"given":"Dan","family":"Chen","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou, Gansu 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongzhou","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou, Gansu 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zebang","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou, Gansu 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gaofeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou, Gansu 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chong","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou, Gansu 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingguo","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou, Gansu 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/0743-7315(91)90113-N","article-title":"The twisted cube topology for multiprocessors: A study in network asymmetry","volume":"13","author":"Abraham","year":"1991","journal-title":"J. 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