{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:19:29Z","timestamp":1758824369444,"version":"3.37.3"},"reference-count":19,"publisher":"EDP Sciences","issue":"1","license":[{"start":{"date-parts":[[2018,5,30]],"date-time":"2018-05-30T00:00:00Z","timestamp":1527638400000},"content-version":"vor","delay-in-days":149,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["P1-0297"],"award-info":[{"award-number":["P1-0297"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2018,1,14]]},"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The strong geodetic problem is a recent variation of the geodetic problem. For a graph <jats:italic>G<\/jats:italic>, its strong geodetic number sg(<jats:italic>G<\/jats:italic>) is the cardinality of a smallest vertex subset <jats:italic>S<\/jats:italic>, such that each vertex of <jats:italic>G<\/jats:italic> lies on a fixed shortest path between a pair of vertices from <jats:italic>S<\/jats:italic>. In this paper, the strong geodetic problem is studied on the Cartesian product of graphs. A general upper bound for sg(<jats:italic>G<\/jats:italic> \u25a1 <jats:italic>H<\/jats:italic>) is determined, as well as exact values for <jats:italic>K<\/jats:italic><jats:sub><jats:italic>m<\/jats:italic><\/jats:sub> \u25a1 <jats:italic>K<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>, <jats:italic>K<\/jats:italic><jats:sub>1,<jats:italic>k<\/jats:italic><\/jats:sub> \u25a1 <jats:italic>P<\/jats:italic><jats:sub><jats:italic>l<\/jats:italic><\/jats:sub>, and prisms over <jats:italic>K<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>\u2013<jats:italic>e<\/jats:italic>. Connections between the strong geodetic number of a graph and its subgraphs are also discussed.<\/jats:p>","DOI":"10.1051\/ro\/2018003","type":"journal-article","created":{"date-parts":[[2018,1,16]],"date-time":"2018-01-16T08:51:59Z","timestamp":1516092719000},"page":"205-216","source":"Crossref","is-referenced-by-count":7,"title":["Strong geodetic problem on Cartesian products of graphs"],"prefix":"10.1051","volume":"52","author":[{"given":"Vesna","family":"Ir\u0161i\u010d","sequence":"first","affiliation":[]},{"given":"Sandi","family":"Klav\u017ear","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2018,5,30]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.2298\/FIL1506361A","volume":"29","author":"Ahangar","year":"2015","journal-title":"Filomat"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Bre\u0161ar B., \nKov\u0161e M. and \nTepeh A., Geodetic sets in graphs, in \nStructural Analysis of Complex Networks. \nBirkh\u00e4user\/Springer, \nNew York \n(2011) 197\u2013218.","DOI":"10.1007\/978-0-8176-4789-6_8"},{"key":"R3","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1137\/110859014","volume":"27","author":"Centeno","year":"2013","journal-title":"SIAM J. 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