{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T14:18:09Z","timestamp":1778595489164,"version":"3.51.4"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:p> An important tool for the execution of parallel algorithms and the simulation of interconnection networks is graph embedding. The quality of an embedding can be assessed using some cost metrics. The dilation and wirelength are the commonly used parameters. The Kn\u00f6del graph [Formula: see text] is a minimum linear gossip network and has minimum broadcasting. It has [Formula: see text] vertices, [Formula: see text] edges, where [Formula: see text] is even, and [Formula: see text]log[Formula: see text]. In this study, we solve the dilation problem of embedding the Kn\u00f6del graph into certain cube-like architectures such as hypercube, folded hypercube, and augmented cube. In [G. Fertin, A. Raspaud, A survey on Kn\u00f6del graphs, Discrete Applied Mathematics\u00a0137 (2004) 173\u2013195], it is proved that the dilation of embedding the Kn\u00f6del graph [Formula: see text] into the hypercube [Formula: see text] is at most [Formula: see text]. In this study, we obtain an improved upper bound for dilation of embedding the Kn\u00f6del graph into the hypercube and it is equal to [Formula: see text]. Also, we calculate the wirelength of embedding the Kn\u00f6del graph into the above-said cube-like architectures using dilation. <\/jats:p>","DOI":"10.1142\/s0219265923500317","type":"journal-article","created":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T14:04:36Z","timestamp":1701093876000},"source":"Crossref","is-referenced-by-count":5,"title":["Embedding Kn\u00f6del Graph into Cube-like Architectures: Dilation Optimization and Wirelength Analysis"],"prefix":"10.1142","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-2120-6237","authenticated-orcid":false,"given":"Remi Mariam","family":"Reji","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai, Chennai, Tamil Nadu 603103, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1851-6334","authenticated-orcid":false,"given":"R.","family":"Sundara Rajan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai, Chennai, Tamil Nadu 603103, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9700-8110","authenticated-orcid":false,"given":"T. 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