{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T03:18:01Z","timestamp":1779247081249,"version":"3.51.4"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,3,10]],"date-time":"2018-03-10T00:00:00Z","timestamp":1520640000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2018,5]]},"DOI":"10.1007\/s00373-018-1885-9","type":"journal-article","created":{"date-parts":[[2018,3,10]],"date-time":"2018-03-10T04:42:30Z","timestamp":1520656950000},"page":"443-456","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Strong Geodetic Number of Complete Bipartite Graphs and of Graphs with Specified Diameter"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5302-5250","authenticated-orcid":false,"given":"Vesna","family":"Ir\u0161i\u010d","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,10]]},"reference":[{"key":"1885_CR1","doi-asserted-by":"publisher","first-page":"1361","DOI":"10.2298\/FIL1506361A","volume":"29","author":"HA Ahangar","year":"2015","unstructured":"Ahangar, H.A., Kosari, S., Sheikholeslami, S.M., Volkmann, L.: Graphs with large geodetic number. Filomat 29, 1361\u20131368 (2015)","journal-title":"Filomat"},{"key":"1885_CR2","doi-asserted-by":"crossref","unstructured":"Bre\u0161ar, B., Kov\u0161e, M., Tepeh, A.: Geodetic sets in graphs. In: Structural Analysis of Complex Networks, pp. 197\u2013218. Birkh\u00e4user\/Springer, New York (2011)","DOI":"10.1007\/978-0-8176-4789-6_8"},{"key":"1885_CR3","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1137\/110859014","volume":"27","author":"CC Centeno","year":"2013","unstructured":"Centeno, C.C., Penso, L.D., Rautenbach, D., Pereira de S\u00e1, V.G.: Geodetic number versus hull number in $$P_3$$ P 3 -convexity. SIAM J. Discr. Math. 27, 717\u2013731 (2013)","journal-title":"SIAM J. Discr. Math."},{"key":"1885_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/net.10007","volume":"39","author":"G Chartrand","year":"2002","unstructured":"Chartrand, G., Harary, F., Zhang, P.: On the geodetic number of a graph. Networks 39, 1\u20136 (2002)","journal-title":"Networks"},{"key":"1885_CR5","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1051\/ro\/2014019","volume":"48","author":"T Ekim","year":"2014","unstructured":"Ekim, T., Erey, A.: Block decomposition approach to compute a minimum geodetic set. RAIRO Oper. Res. 48, 497\u2013507 (2014)","journal-title":"RAIRO Oper. Res."},{"key":"1885_CR6","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/978-3-642-29344-3_24","volume":"7256","author":"T Ekim","year":"2012","unstructured":"Ekim, T., Erey, A., Heggernes, P., van \u2019t\u00a0Hof, P., Meister, D.: Computing minimum geodetic sets in proper interval graphs. Lect. Notes Comput. Sci. 7256, 279\u2013290 (2012)","journal-title":"Lect. Notes Comput. Sci."},{"key":"1885_CR7","first-page":"97","volume":"38","author":"DC Fisher","year":"2001","unstructured":"Fisher, D.C., Fitzpatrick, S.L.: The isometric path number of a graph. J. Combin. Math. Combin. Comput. 38, 97\u2013110 (2001)","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"1885_CR8","first-page":"109","volume":"137","author":"SL Fitzpatrick","year":"1999","unstructured":"Fitzpatrick, S.L.: Isometric path number of the Cartesian product of paths. Congr. Numer. 137, 109\u2013119 (1999)","journal-title":"Congr. Numer."},{"key":"1885_CR9","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/BF01254296","volume":"18","author":"AS Fraenkel","year":"1989","unstructured":"Fraenkel, A.S., Harary, F.: Geodetic contraction games on graphs. Int. J. Game Theory 18, 327\u2013338 (1989)","journal-title":"Int. J. Game Theory"},{"key":"1885_CR10","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/0895-7177(93)90259-2","volume":"17","author":"F Harary","year":"1993","unstructured":"Harary, F., Loukakis, E., Tsouros, C.: The geodetic number of a graph. Math. Comput. Model. 17, 89\u201395 (1993)","journal-title":"Math. Comput. Model."},{"key":"1885_CR11","unstructured":"Jiang, T., Pelayo, I.M., Pritikin, D.: Geodesic convexity and Cartesian products in graphs. Manuscript (2004)"},{"key":"1885_CR12","doi-asserted-by":"publisher","unstructured":"Klav\u017ear, S., Manuel, P.: Strong geodetic problem in grid like architectures. To appear Bull. Malays. Math. Sci. Soc. https:\/\/doi.org\/10.1007\/s40840-018-0609-x","DOI":"10.1007\/s40840-018-0609-x"},{"key":"1885_CR13","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1007\/s11425-007-0048-x","volume":"50","author":"C Lu","year":"2007","unstructured":"Lu, C.: The geodetic numbers of graphs and digraphs. Sci. Chin. Ser. A 50, 1163\u20131172 (2007)","journal-title":"Sci. Chin. Ser. A"},{"key":"1885_CR14","doi-asserted-by":"crossref","unstructured":"Manuel, P., Klav\u017ear, S., Xavier, A., Arokiaraj, A., Thomas, E.: Strong geodetic problem in networks: computational complexity and solution for Apollonian networks. Submitted (2016)","DOI":"10.1515\/math-2017-0101"},{"key":"1885_CR15","doi-asserted-by":"publisher","first-page":"1225","DOI":"10.1515\/math-2017-0101","volume":"15","author":"P Manuel","year":"2017","unstructured":"Manuel, P., Klav\u017ear, S., Xavier, A., Arokiaraj, A., Thomas, E.: Strong edge geodetic problem in networks. Open Math. 15, 1225\u20131235 (2017)","journal-title":"Open Math."},{"key":"1885_CR16","doi-asserted-by":"publisher","first-page":"2091","DOI":"10.1016\/j.disc.2006.04.003","volume":"306","author":"J-J Pan","year":"2006","unstructured":"Pan, J.-J., Chang, G.J.: Isometric path numbers of graphs. Discr. Math. 306, 2091\u20132096 (2006)","journal-title":"Discr. Math."},{"key":"1885_CR17","series-title":"Springer Briefs in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-8699-2","volume-title":"Geodesic Convexity in Graphs","author":"IM Pelayo","year":"2013","unstructured":"Pelayo, I.M.: Geodesic Convexity in Graphs. Springer Briefs in Mathematics. Springer, New York (2013)"},{"key":"1885_CR18","first-page":"415","volume":"10","author":"AP Santhakumaran","year":"2007","unstructured":"Santhakumaran, A.P., John, J.: Edge geodetic number of a graph. J. Discr. Math. Sci. Cryprogr. 10, 415\u2013432 (2007)","journal-title":"J. Discr. Math. Sci. Cryprogr."},{"key":"1885_CR19","first-page":"67","volume":"17","author":"AP Santhakumaran","year":"2009","unstructured":"Santhakumaran, A.P., John, J.: The connected edge geodetic number of a graph. Sci. Ser. A Math. Sci. (N.S.) 17, 67\u201382 (2009)","journal-title":"Sci. Ser. A Math. Sci. (N.S.)"},{"key":"1885_CR20","doi-asserted-by":"publisher","first-page":"35","DOI":"10.7151\/dmgt.1774","volume":"35","author":"JA Soloff","year":"2015","unstructured":"Soloff, J.A., M\u00e1rquez, R.A., Friedler, L.M.: Products of geodesic graphs and the geodetic number of products. Discuss. Math. Graph Theory 35, 35\u201342 (2015)","journal-title":"Discuss. Math. Graph Theory"}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00373-018-1885-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-018-1885-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-018-1885-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,12]],"date-time":"2019-10-12T12:57:53Z","timestamp":1570885073000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00373-018-1885-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,10]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,5]]}},"alternative-id":["1885"],"URL":"https:\/\/doi.org\/10.1007\/s00373-018-1885-9","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"value":"0911-0119","type":"print"},{"value":"1435-5914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,10]]},"assertion":[{"value":"20 July 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}