{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:44:28Z","timestamp":1762325068808,"version":"3.37.3"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,7,31]],"date-time":"2021-07-31T00:00:00Z","timestamp":1627689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,7,31]],"date-time":"2021-07-31T00:00:00Z","timestamp":1627689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671037"],"award-info":[{"award-number":["11671037"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2022,3]]},"DOI":"10.1007\/s10878-021-00780-8","type":"journal-article","created":{"date-parts":[[2021,7,31]],"date-time":"2021-07-31T18:02:48Z","timestamp":1627754568000},"page":"460-496","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Determining the edge metric dimension of the generalized Petersen graph P(n,\u00a03)"],"prefix":"10.1007","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7478-7422","authenticated-orcid":false,"given":"David G. L.","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Monica M. Y.","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiqiang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,7,31]]},"reference":[{"key":"780_CR1","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1016\/0095-8956(83)90042-4","volume":"34","author":"B Alspach","year":"1983","unstructured":"Alspach B (1983) The classification of Hamiltonian generalized Petersen graphs. J Combin Theory Ser B 34:293\u2013312","journal-title":"J Combin Theory Ser B"},{"key":"780_CR2","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/S0095-8956(81)80026-3","volume":"31","author":"B Alspach","year":"1981","unstructured":"Alspach B, Robinson PJ, Rosenfeld M (1981) A result on Hamiltonian cycles in generalized Petersen graphs. J Combin Theory Ser B 31:225\u2013231","journal-title":"J Combin Theory Ser B"},{"key":"780_CR3","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/0095-8956(78)90019-9","volume":"24","author":"K Bannai","year":"1978","unstructured":"Bannai K (1978) Hamiltonian cycles in generalized Petersen graphs. J Combin Theory Ser B 24:181\u2013188","journal-title":"J Combin Theory Ser B"},{"key":"780_CR4","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1016\/j.disc.2007.03.024","volume":"308","author":"A Behzad","year":"2008","unstructured":"Behzad A, Behzad M, Praeger CE (2008) On the domination number of the generalized Petersen graphs. Discrete Math 308:603\u2013610","journal-title":"Discrete Math"},{"key":"780_CR5","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1002\/jcd.20054","volume":"13","author":"M Boben","year":"2005","unstructured":"Boben M, Pisanski T, \u017ditnik A (2005) $$I$$-Graphs and the corresponding configurations. J Combin Des 13:406\u2013424","journal-title":"J Combin Des"},{"key":"780_CR6","doi-asserted-by":"publisher","first-page":"2394","DOI":"10.1016\/j.dam.2007.07.018","volume":"155","author":"B Bre\u0161ara","year":"2007","unstructured":"Bre\u0161ara B, \u0160umenjakb TK (2007) On the 2-rainbow domination in graphs. Discrete Appl Math 155:2394\u20132400","journal-title":"Discrete Appl Math"},{"key":"780_CR7","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/0012-365X(92)90649-Z","volume":"100","author":"G Chartrand","year":"1992","unstructured":"Chartrand G, Hevia H, Wilson RJ (1992) The ubiquitous Petersen graph. Discrete Math 100:303\u2013311","journal-title":"Discrete Math"},{"key":"780_CR8","volume-title":"Introduction to Algorithms","author":"TH Cormen","year":"2009","unstructured":"Cormen TH, Leiserson CE, Rivest RL, Stein CC (2009) Introduction to Algorithms. MIT press, London"},{"key":"780_CR9","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1090\/S0002-9904-1950-09407-5","volume":"56","author":"HSM Coxeter","year":"1950","unstructured":"Coxeter HSM (1950) Self-dual configurations and regular graphs. Bull. Amer. Math. Soc. 56:413\u2013455","journal-title":"Bull. Amer. Math. Soc."},{"key":"780_CR10","doi-asserted-by":"publisher","first-page":"53","DOI":"10.2140\/pjm.1972.40.53","volume":"40","author":"F Castagna","year":"1972","unstructured":"Castagna F, Prins G (1972) Every generalized Petersen graph has a Tait coloring. Pacific J Math 40:53\u201358","journal-title":"Pacific J Math"},{"key":"780_CR11","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1007\/s10878-016-0013-0","volume":"33","author":"A Daneshgar","year":"2017","unstructured":"Daneshgar A, Madani M (2017) On the odd girth and the circular chromatic number of generalized Petersen graphs. J Comb Optim 33:897\u2013923","journal-title":"J Comb Optim"},{"key":"780_CR12","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/j.dam.2017.02.002","volume":"252","author":"GB Ekinci","year":"2019","unstructured":"Ekinci GB, Gauci JB (2019) On the reliability of generalized Petersen graphs. Discrete Appl Math 252:2\u20139","journal-title":"Discrete Appl Math"},{"key":"780_CR13","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1017\/S0305004100049811","volume":"70","author":"R Frucht","year":"1971","unstructured":"Frucht R, Graver JE, Watkins ME (1971) The groups of the generalized Petersen graphs. Proc Cambridge Philos Soc 70:211\u2013218","journal-title":"Proc Cambridge Philos Soc"},{"key":"780_CR14","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1007\/s00025-019-1105-9","volume":"74","author":"V Filipovi\u0107","year":"2019","unstructured":"Filipovi\u0107 V, Kartelj A, Kratica J (2019) Edge metric dimension of some generalized Petersen graphs. Results Math 74:182","journal-title":"Results Math"},{"issue":"4","key":"780_CR15","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/j.jctb.2005.09.009","volume":"96","author":"P Hlin\u011bn\u00fd","year":"2006","unstructured":"Hlin\u011bn\u00fd P (2006) Crossing number is hard for cubic graphs. J Combin Theory Ser B 96(4):455\u2013471","journal-title":"J Combin Theory Ser B"},{"key":"780_CR16","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662058","volume-title":"The Petersen graph","author":"DA Holton","year":"1993","unstructured":"Holton DA, Sheehan J (1993) The Petersen graph. Cambridge University Press, Cambridge"},{"key":"780_CR17","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/j.dam.2018.12.011","volume":"266","author":"DDD Jin","year":"2019","unstructured":"Jin DDD, Wang DGL (2019) On the minimum vertex cover of generalized Petersen graphs. Discrete Appl Math 266:309\u2013318","journal-title":"Discrete Appl Math"},{"key":"780_CR18","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.amc.2017.07.027","volume":"314","author":"A Kelenc","year":"2017","unstructured":"Kelenc A, Kuziak D, Taranenko A, Yero IG (2017) Mixed metric dimension of graphs. Appl Math Comput 314:429\u2013438","journal-title":"Appl Math Comput"},{"key":"780_CR19","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/j.laa.2017.04.032","volume":"529","author":"YS Kwon","year":"2017","unstructured":"Kwon YS, Mednykh AD, Mednykh IA (2017) On Jacobian group and complexity of the generalized Petersen graph $$\\rm GP(n, k)$$ through Chebyshev polynomials. Linear Algebra Appl 529:355\u2013373","journal-title":"Linear Algebra Appl"},{"key":"780_CR20","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1016\/j.dam.2018.05.052","volume":"251","author":"A Kelenc","year":"2018","unstructured":"Kelenc A, Tratnik N, Yero IG (2018) Uniquely identifying the edges of a graph: the edge metric dimension. Discrete Appl Math 251:204\u2013220","journal-title":"Discrete Appl Math"},{"key":"780_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2020.03.007","author":"M Krnc","year":"2020","unstructured":"Krnc M, Wilson RJ (2020) Recognizing generalized Petersen graphs in linear time. Math Discrete Appl. https:\/\/doi.org\/10.1016\/j.dam.2020.03.007","journal-title":"Math Discrete Appl"},{"key":"780_CR22","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1006\/jctb.1997.1729","volume":"69","author":"M Lovre\u010di\u010d Sara\u017ein","year":"1997","unstructured":"Lovre\u010di\u010d Sara\u017ein M (1997) A note on the generalized Petersen graphs that are also Cayley graphs. J Combin Theory Ser B 69:226\u2013229","journal-title":"J Combin Theory Ser B"},{"key":"780_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/jgt.3190190102","volume":"19","author":"R Nedela","year":"1995","unstructured":"Nedela R, \u0160koviera M (1995) Which generalized Petersen graphs are Cayley graphs? J Graph Theory 19:1\u201311","journal-title":"J Graph Theory"},{"key":"780_CR24","doi-asserted-by":"publisher","first-page":"2465","DOI":"10.1007\/s40840-019-00816-7","volume":"43","author":"I Peterin","year":"2020","unstructured":"Peterin I, Yero IG (2020) Edge metric dimension of some graph operations. Bull Malaysia Math Sci Soc 43:2465\u20132477","journal-title":"Bull Malaysia Math Sci Soc"},{"key":"780_CR25","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/s003730200028","volume":"18","author":"RB Richter","year":"2002","unstructured":"Richter RB, Salazar G (2002) The crossing number of $$P(N,3)$$. Graphs Combin 18:381\u2013394","journal-title":"Graphs Combin"},{"key":"780_CR26","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0095-8956(89)90064-6","volume":"47","author":"AJ Schwenk","year":"1989","unstructured":"Schwenk AJ (1989) Enumeration of Hamiltonian cycles in certain generalized Petersen graphs. J Combin Theory Ser B 47:53\u201359","journal-title":"J Combin Theory Ser B"},{"key":"780_CR27","first-page":"549","volume":"14","author":"PJ Slater","year":"1975","unstructured":"Slater PJ (1975) Leaves of trees. Congr Numer 14:549\u2013559","journal-title":"Congr Numer"},{"key":"780_CR28","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/0095-8956(84)90068-6","volume":"47","author":"S Stueckle","year":"1984","unstructured":"Stueckle S, Ringeisen RD (1984) Generalized Petersen graphs which are cycle permutation graphs. J Combin Theory Ser B 47:142\u2013150","journal-title":"J Combin Theory Ser B"},{"key":"780_CR29","unstructured":"Tutte WT (1967) A geometrical version of the four color problem, in book: combinatorial mathematics and its applications (Monographs on Statistics and Applied Probability). In: RC Bose, TA Dowling (eds.) Proceedings of the conference held at the University North Carolina at Chapel Hill, April 10th\u201314th, UNC Press, Chapel Hill, 2011 (originally published in 1969)"},{"key":"780_CR30","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1016\/S0021-9800(69)80116-X","volume":"6","author":"ME Watkins","year":"1969","unstructured":"Watkins ME (1969) A theorem on Tait colorings with an application to the generalized Petersen graphs. J Combin Theory 6:152\u2013164","journal-title":"J Combin Theory"},{"key":"780_CR31","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1007\/s10878-010-9293-y","volume":"22","author":"G Xu","year":"2011","unstructured":"Xu G, Kang L (2011) On the power domination number of the generalized Petersen graphs. J Comb Optim 22:282\u2013291","journal-title":"J Comb Optim"},{"key":"780_CR32","doi-asserted-by":"publisher","first-page":"2570","DOI":"10.1016\/j.dam.2009.03.016","volume":"157","author":"G Xu","year":"2009","unstructured":"Xu G (2009) 2-rainbow domination in generalized Petersen graphs $$P(n,3)$$. Discrete Appl Math 157:2570\u20132573","journal-title":"Discrete Appl Math"},{"key":"780_CR33","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.endm.2016.10.047","volume":"55","author":"IG Yero","year":"2016","unstructured":"Yero IG (2016) Vertices, edges, distances and metric dimension in graphs. Electron Notes Discrete Math 55:191\u2013194","journal-title":"Electron Notes Discrete Math"},{"key":"780_CR34","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.amc.2017.10.047","volume":"321","author":"Z Yang","year":"2018","unstructured":"Yang Z, Wu B (2018) Strong edge chromatic index of the generalized Petersen graphs. Appl Math Comput 321:431\u2013441","journal-title":"Appl Math Comput"},{"key":"780_CR35","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/j.dam.2018.08.031","volume":"257","author":"E Zhu","year":"2019","unstructured":"Zhu E, Taranenko A, Shao Z, Xu J (2019) On graphs with the maximum edge metric dimension. Discrete Appl Math 257:317\u2013324","journal-title":"Discrete Appl Math"},{"issue":"7","key":"780_CR36","doi-asserted-by":"publisher","first-page":"2083","DOI":"10.1016\/j.disc.2018.04.010","volume":"341","author":"N Zubrilina","year":"2018","unstructured":"Zubrilina N (2018) On the edge dimension of a graph. Discrete Math 341(7):2083\u20132088","journal-title":"Discrete Math"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-021-00780-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10878-021-00780-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-021-00780-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T18:52:58Z","timestamp":1699296778000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10878-021-00780-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,31]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["780"],"URL":"https:\/\/doi.org\/10.1007\/s10878-021-00780-8","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"type":"print","value":"1382-6905"},{"type":"electronic","value":"1573-2886"}],"subject":[],"published":{"date-parts":[[2021,7,31]]},"assertion":[{"value":"8 July 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 July 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}