{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:51:49Z","timestamp":1753883509598,"version":"3.41.2"},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,4,12]],"date-time":"2011-04-12T00:00:00Z","timestamp":1302566400000},"content-version":"vor","delay-in-days":101,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>A number of graph coloring problems have their roots in a communication problem known as the channel assignment problem. The channel assignment problem is the problem of assigning channels (nonnegative integers) to the stations in an optimal way such that\ninterference is avoided as reported by Hale (2005). Radio <jats:italic>k<\/jats:italic>\u2010coloring of a graph is a special type of channel assignment problem. Kchikech et al. (2005) have given a lower and an upper bound for radio <jats:italic>k<\/jats:italic>\u2010chromatic number of hypercube <jats:italic>Q<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, and an improvement of their lower bound was obtained by Kola and Panigrahi (2010). In this paper, we further improve Kola et al.\u2032s lower bound as well as Kchikeck et al.\u2032s upper bound. Also, our bounds agree for nearly antipodal number of <jats:italic>Q<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> when <jats:italic>n<\/jats:italic> \u2261 2 (mod 4).<\/jats:p>","DOI":"10.1155\/2011\/961649","type":"journal-article","created":{"date-parts":[[2011,4,12]],"date-time":"2011-04-12T19:33:51Z","timestamp":1302636831000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Improved Bounds for Radio <i>k<\/i>\u2010Chromatic Number of Hypercube <i>Q<\/i><sub><i>n<\/i><\/sub>"],"prefix":"10.1155","volume":"2011","author":[{"given":"Laxman","family":"Saha","sequence":"first","affiliation":[]},{"given":"Pratima","family":"Panigrahi","sequence":"additional","affiliation":[]},{"given":"Pawan","family":"Kumar","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,4,12]]},"reference":[{"key":"e_1_2_5_1_2","first-page":"43","article-title":"A graph labeling problem suggested by FM channel restrictions","volume":"43","author":"Chartrand G.","year":"2005","journal-title":"Bulletin of the Institute of Combinatorics and Its Applications"},{"key":"e_1_2_5_2_2","first-page":"307","article-title":"Radio number for square paths","volume":"90","author":"Liu D. 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In press.","key":"e_1_2_5_6_2"},{"doi-asserted-by":"publisher","key":"e_1_2_5_7_2","DOI":"10.1016\/j.camwa.2010.07.058"},{"doi-asserted-by":"publisher","key":"e_1_2_5_8_2","DOI":"10.21136\/MB.2005.134100"},{"doi-asserted-by":"publisher","key":"e_1_2_5_9_2","DOI":"10.21136\/MB.2009.140642"},{"key":"e_1_2_5_10_2","first-page":"209","article-title":"On radio (n \u2212 4)-chromatic number of the path P\n                  \n                     n","volume":"6","author":"Kola S. R.","year":"2009","journal-title":"AKCE International Journal of Graphs and Combinatorics"},{"unstructured":"JuanJ. S.andLiuD. D.-F. 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