{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T18:48:38Z","timestamp":1773514118200,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2011,2,1]],"date-time":"2011-02-01T00:00:00Z","timestamp":1296518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As wireless mobile telecommunication bases organize their structure using a honeycomb-mesh algorithm, there are many studies about parallel processing algorithms like the honeycomb mesh in Wireless Sensor Networks. This paper aims to study the Peterson-Torus graph algorithm in regard to the continuity with honeycomb-mesh algorithm in order to apply the algorithm to sensor networks. Once a new interconnection network is designed, parallel algorithms are developed with huge research costs to use such networks. If the old network is embedded in a newly designed network, a developed algorithm in the old network is reusable in a newly designed network. Petersen-Torus has been designed recently, and the honeycomb mesh has already been designed as a well-known interconnection network. In this paper, we propose a one-to-one embedding algorithm for the honeycomb mesh (HMn) in the Petersen-Torus PT(n,n), and prove that dilation of the algorithm is 5, congestion is 2, and expansion is 5\/3. The proposed one-to-one embedding is applied so that processor throughput can be minimized when the honeycomb mesh algorithm runs in the Petersen-Torus.<\/jats:p>","DOI":"10.3390\/s110201959","type":"journal-article","created":{"date-parts":[[2011,2,1]],"date-time":"2011-02-01T11:24:19Z","timestamp":1296559459000},"page":"1959-1971","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["One-to-One Embedding between Honeycomb Mesh and Petersen-Torus Networks"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2117-5750","authenticated-orcid":false,"given":"Jung-Hyun","family":"Seo","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, National University of Sunchon, Maegok 315, Sunchon, Jeonnam, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hyun","family":"Sim","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, National University of Sunchon, Maegok 315, Sunchon, Jeonnam, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dae-Heon","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Information and Communication Engineering, National University of Sunchon, Maegok 315, Sunchon, Jeonnam, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jang-Woo","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Information and Communication Engineering, National University of Sunchon, Maegok 315, Sunchon, Jeonnam, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang-Sun","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Information and Communication Engineering, Chosun Universtiy, 375 Seosuk-Dong, Dong-Gu, Gwangju, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2011,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1109\/71.485505","article-title":"Folded Petersen cube networks: New competitors for the hypercubes","volume":"7","author":"Ohring","year":"1996","journal-title":"IEEE Trans. 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