{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:16:25Z","timestamp":1753884985637,"version":"3.41.2"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100005276","name":"National Board for Higher Mathematics","doi-asserted-by":"publisher","award":["NBHM\/R.P.29\/2015\/Fresh\/157."],"award-info":[{"award-number":["NBHM\/R.P.29\/2015\/Fresh\/157."]}],"id":[{"id":"10.13039\/501100005276","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> For a connected graph G of order at least two, a double geodetic set S of a graph G is a restrained double geodetic set if either [Formula: see text] or the subgraph induced by [Formula: see text] has no isolated vertices. The minimum cardinality of a restrained double geodetic set of G is the restrained double geodetic number of G and is denoted by [Formula: see text]. The restrained double geodetic number of some standard graphs is determined. It is proved that for a nontrivial connected graph [Formula: see text] [Formula: see text] if and only if [Formula: see text]. It is shown that for any three positive integers [Formula: see text] with [Formula: see text], there is a connected graph [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] is the geodetic number and [Formula: see text] is the restrained geodetic number of a graph G. It is also shown that for every pair a, b of positive integers with [Formula: see text], there is a connected graph [Formula: see text] with [Formula: see text] and [Formula: see text], where [Formula: see text] is the double geodetic number of a graph G. <\/jats:p>","DOI":"10.1142\/s1793830922501002","type":"journal-article","created":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T15:08:03Z","timestamp":1650380883000},"source":"Crossref","is-referenced-by-count":1,"title":["The restrained double geodetic number of a graph"],"prefix":"10.1142","volume":"15","author":[{"given":"A. P.","family":"Santhakumaran","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603 103, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2769-1991","authenticated-orcid":false,"given":"K.","family":"Ganesamoorthy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Coimbatore Institute of Technology, Coimbatore 641 014, India"}]}],"member":"219","published-online":{"date-parts":[[2022,5,10]]},"reference":[{"key":"S1793830922501002BIB001","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1007\/s40840-014-0068-y","volume":"38","author":"Abdollahzadeh Ahangar H.","year":"2015","journal-title":"Bull. Malays. Math. Sci. Soc."},{"volume-title":"Distance in Graphs","year":"1990","author":"Buckley F.","key":"S1793830922501002BIB002"},{"key":"S1793830922501002BIB003","first-page":"51","volume":"31","author":"Chartrand G.","year":"2001","journal-title":"Bull. Inst. Combin. Appl."},{"issue":"1","key":"S1793830922501002BIB004","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/net.10007","volume":"39","author":"Chartrand G.","year":"2002","journal-title":"Networks"},{"key":"S1793830922501002BIB005","first-page":"3","volume":"72","author":"Chartrand G.","year":"2004","journal-title":"Ars Combin."},{"issue":"122","key":"S1793830922501002BIB006","doi-asserted-by":"crossref","first-page":"79","DOI":"10.2298\/PIM2022079G","volume":"108","author":"Ganesamoorthy K.","year":"2020","journal-title":"Publ. Inst. Math."},{"issue":"2","key":"S1793830922501002BIB007","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s40010-020-00661-5","volume":"91","author":"Ganesamoorthy K.","year":"2021","journal-title":"Proc. Natl. Acad. Sci. India Sect. A Phys. Sci."},{"key":"S1793830922501002BIB008","doi-asserted-by":"crossref","DOI":"10.21236\/AD0705364","volume-title":"Graph Theory","author":"Harary F.","year":"1969"},{"issue":"11","key":"S1793830922501002BIB009","first-page":"87","volume":"17","author":"Harary F.","year":"1993","journal-title":"Math. Comput. Modelling"},{"key":"S1793830922501002BIB010","first-page":"161","volume":"143","author":"Muntean R.","year":"2000","journal-title":"Congr. Numer."},{"key":"S1793830922501002BIB011","doi-asserted-by":"crossref","first-page":"109","DOI":"10.7151\/dmgt.1589","volume":"32","author":"Santhakumaran A. P.","year":"2012","journal-title":"Discuss. Math. Graph Theory"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922501002","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T10:16:01Z","timestamp":1679652961000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922501002"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,10]]},"references-count":11,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["10.1142\/S1793830922501002"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922501002","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,5,10]]},"article-number":"2250100"}}