{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:31Z","timestamp":1740144511098,"version":"3.37.3"},"reference-count":19,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T00:00:00Z","timestamp":1614643200000},"content-version":"vor","delay-in-days":60,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"funder":[{"name":"nil"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2020,6,26]]},"published-print":{"date-parts":[[2021]]},"abstract":"<jats:p>Let <jats:italic>G<\/jats:italic> = (<jats:italic>V, E<\/jats:italic>) be a simple connected graph of order <jats:italic>p<\/jats:italic> and size <jats:italic>q<\/jats:italic>. A decomposition of a graph <jats:italic>G<\/jats:italic> is a collection <jats:italic>\u03c0<\/jats:italic> of edge-disjoint subgraphs <jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub>, \u2026 , <jats:italic>G<jats:sub>n<\/jats:sub><\/jats:italic> of <jats:italic>G<\/jats:italic> such that every edge of <jats:italic>G<\/jats:italic> belongs to exactly one <jats:italic>G<jats:sub>i<\/jats:sub><\/jats:italic>(1 \u2264 <jats:italic>i<\/jats:italic> \u2264 <jats:italic>n<\/jats:italic>). The decomposition <jats:italic>\u03c0<\/jats:italic> = {<jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub>, \u2026 , <jats:italic>G<jats:sub>n<\/jats:sub><\/jats:italic>} of a connected graph <jats:italic>G<\/jats:italic> is said to be an edge geodetic self decomposition, if <jats:italic>g<jats:sub>e<\/jats:sub><\/jats:italic>(<jats:italic>G<jats:sub>i<\/jats:sub><\/jats:italic>) = <jats:italic>g<jats:sub>e<\/jats:sub><\/jats:italic>(<jats:italic>G<\/jats:italic>) for all <jats:italic>i<\/jats:italic>(1 \u2264 <jats:italic>i<\/jats:italic> \u2264 <jats:italic>n<\/jats:italic>). The maximum cardinality of <jats:italic>\u03c0<\/jats:italic> is called the edge geodetic self decomposition number of <jats:italic>G<\/jats:italic> and is denoted by <jats:italic>\u03c0<jats:sub>sg<jats:sub>e<\/jats:sub><\/jats:sub><\/jats:italic>(<jats:italic>G<\/jats:italic>), where <jats:italic>g<jats:sub>e<\/jats:sub><\/jats:italic>(<jats:italic>G<\/jats:italic>) is the edge geodetic number of <jats:italic>G<\/jats:italic>. Some general properties satisfied by this concept are studied.<\/jats:p>","DOI":"10.1051\/ro\/2020073","type":"journal-article","created":{"date-parts":[[2020,6,30]],"date-time":"2020-06-30T19:49:41Z","timestamp":1593546581000},"page":"S1935-S1947","source":"Crossref","is-referenced-by-count":1,"special_numbering":"Supplement","title":["The edge geodetic self decomposition number of a graph"],"prefix":"10.1051","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4715-5638","authenticated-orcid":false,"given":"J.","family":"John","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"Stalin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2021,3,2]]},"reference":[{"key":"R1","first-page":"45","volume":"4","author":"Arul Paul Sudhahar","year":"2016","journal-title":"Int. J. Math. 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