{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T13:29:33Z","timestamp":1742390973431},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"03n04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:p> We present some results concerning hamiltonian properties of recursive circulant graphs in the presence of faulty vertices and\/or edges. The recursive circulant graph G(N, d) with d \u2265 2 has vertex set V(G) = {0, 1, \u2026, N - 1} and the edge set E(G) = {(v, w)| \u2203 i, 0 \u2264 i \u2264 \u2308 log <jats:sub>d<\/jats:sub> N\u2309 - 1, such that v = w + d<jats:sup>i<\/jats:sup> (mod N)}. When N = cd<jats:sup>k<\/jats:sup> where d \u2265 2 and 2 \u2264 c \u2264 d, G(cd<jats:sup>k<\/jats:sup>, d) is regular, node symmetric and can be recursively constructed. G(cd<jats:sup>k<\/jats:sup>, d) is a bipartite graph if and only if c is even and d is odd. Let F, the faulty set, be a subset of V(G(cd<jats:sup>k<\/jats:sup>, d)) \u222a E(G(cd<jats:sup>k<\/jats:sup>, d)). In this paper, we prove that G(cd<jats:sup>k<\/jats:sup>, d) - F remains hamiltonian if |F| \u2264 deg (G(cd<jats:sup>k<\/jats:sup>, d)) - 2 and G(cd<jats:sup>k<\/jats:sup>, d) is not bipartite. Moreover, if |F| \u2264 deg (G(cd<jats:sup>k<\/jats:sup>, d)) - 3 and G(cd<jats:sup>k<\/jats:sup>, d) is not a bipartite graph, we prove a more stronger result that for any two vertices u and v in V(G(cd<jats:sup>k<\/jats:sup>, d)) - F, there exists a hamiltonian path of G(cd<jats:sup>k<\/jats:sup>, d) - F joining u and v. <\/jats:p>","DOI":"10.1142\/s0219265902000677","type":"journal-article","created":{"date-parts":[[2003,2,13]],"date-time":"2003-02-13T10:25:38Z","timestamp":1045131938000},"page":"273-289","source":"Crossref","is-referenced-by-count":20,"title":["HAMILTONIAN PROPERTIES OF FAULTY RECURSIVE CIRCULANT GRAPHS"],"prefix":"10.1142","volume":"03","author":[{"given":"CHANG-HSIUNG","family":"TSAI","sequence":"first","affiliation":[{"name":"Department of Computer Science and Information Engineering Dahan Institute of Technology, Hualien, Taiwan 971, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIMMY J. M.","family":"TAN","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Science National Chiao Tung University, Hsinchu, Taiwan 300, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YEN-CHU","family":"CHUANG","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Science National Chiao Tung University, Hsinchu, Taiwan 300, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LIH-HSING","family":"HSU","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Science National Chiao Tung University, Hsinchu, Taiwan 300, R.O.C"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,8]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(99)00199-5"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.6"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.2001.1813"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1109\/71.755822"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(95)00078-6"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(97)00020-3"},{"key":"p_8","first-page":"73","author":"Park J. H.","year":"1994","journal-title":"New York"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(00)00176-6"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265902000677","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:15:33Z","timestamp":1565111733000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219265902000677"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":8,"journal-issue":{"issue":"03n04","published-online":{"date-parts":[[2012,4,8]]},"published-print":{"date-parts":[[2002,9]]}},"alternative-id":["10.1142\/S0219265902000677"],"URL":"https:\/\/doi.org\/10.1142\/s0219265902000677","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}