{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T05:46:53Z","timestamp":1723096013282},"reference-count":0,"publisher":"Combinatorial Press","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>In this paper, we investigate the  ( d , 1 ) -total labelling of generalized Petersen graphs  P ( n , k )  for  d \u2265 3 . We find that the  ( d , 1 ) -total number of  P ( n , k )  with  d \u2265 3  is  d + 3  for even  n  and odd  k  or even  n  and  k = n 2 , and  d + 4  for all other cases.<\/jats:p>","DOI":"10.61091\/ars158-02","type":"journal-article","created":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T22:33:20Z","timestamp":1713134000000},"page":"11-17","source":"Crossref","is-referenced-by-count":0,"title":["\\((d,1)\\)-Total Labelling of Generalized Petersen Graphs \\(P(n,k)\\)"],"prefix":"10.61091","volume":"158","author":[{"name":"College of Information Science and Electricity Engineering, Shandong Jiaotong University, Jinan 250357, China","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunling","family":"Tong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Senyuan","family":"Su","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"College of Computer Science, Dalian University of Technology, Dalian 116024, China","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuansheng","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"College of Computer Science, Dalian University of Technology, Dalian 116024, China","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T22:33:22Z","timestamp":1713134002000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-158\/d1-total-labelling-of-generalized-petersen-graphs-pnk\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2024,3,31]]},"published-print":{"date-parts":[[2024,3,31]]}},"URL":"https:\/\/doi.org\/10.61091\/ars158-02","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"type":"print","value":"0381-7032"},{"type":"electronic","value":"2817-5204"}],"subject":[],"published":{"date-parts":[[2024,1]]}}}