{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T01:50:41Z","timestamp":1648691441559},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:p> For two vertices [Formula: see text] and [Formula: see text] in a connected graph [Formula: see text], the signal distance [Formula: see text] from [Formula: see text] to [Formula: see text] is defined by [Formula: see text], where [Formula: see text] is a path connecting [Formula: see text] and [Formula: see text], [Formula: see text] is the length of the path [Formula: see text] and in the sum [Formula: see text] runs over all the internal vertices between [Formula: see text] and [Formula: see text] in the path [Formula: see text]. A path between the vertices [Formula: see text] and [Formula: see text] of length [Formula: see text] is called a [Formula: see text] geosig path. A set [Formula: see text] is called a signal set, if every vertex [Formula: see text] in [Formula: see text] lies on a geosig path joining a pair of vertices of [Formula: see text]. The signal number [Formula: see text] is the minimum order of a signal set of a graph [Formula: see text]. An edge signal cover of [Formula: see text] is a set [Formula: see text] such that every edge of [Formula: see text] is contained in a geosig path joining some pair of vertices of [Formula: see text]. The edge signal number [Formula: see text] of [Formula: see text] is the minimum order of an edge signal cover and any edge signal cover of order [Formula: see text] is an edge signal basis of [Formula: see text]. In this paper, we initiate a study on the edge signal number of a graph [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830921500245","type":"journal-article","created":{"date-parts":[[2020,10,31]],"date-time":"2020-10-31T04:23:03Z","timestamp":1604118183000},"page":"2150024","source":"Crossref","is-referenced-by-count":0,"title":["The edge signal number of a graph"],"prefix":"10.1142","volume":"13","author":[{"given":"S.","family":"Balamurugan","sequence":"first","affiliation":[{"name":"Department of Mathematics, St. Xavier\u2019s College (Autonomous), Palayamkottai, India"}]},{"given":"R.","family":"Antony Doss","sequence":"additional","affiliation":[{"name":"Manonmaniam Sundaranar University, Tirunelveli, India"}]}],"member":"219","published-online":{"date-parts":[[2020,10,30]]},"reference":[{"key":"S1793830921500245BIB002","volume-title":"Distance in Graphs","author":"Buckley F.","year":"1960"},{"key":"S1793830921500245BIB003","first-page":"75","volume":"53","author":"Chartrand G.","year":"2005","journal-title":"J. Combin. Math. Combin, Comput."},{"key":"S1793830921500245BIB004","volume-title":"Introduction to Graph Theory","author":"Chartrand G.","year":"2011","edition":"7"},{"key":"S1793830921500245BIB005","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1978-079-5"},{"key":"S1793830921500245BIB006","first-page":"50","volume-title":"Algebra, Graph Theory and their Application","author":"Kathiresan K. M.","year":"2010"},{"key":"S1793830921500245BIB007","first-page":"73","volume":"61","author":"Kathiresan K. M.","year":"2007","journal-title":"J. Combin. Math. Combin. Comput."},{"issue":"9","key":"S1793830921500245BIB008","first-page":"53","volume":"2","author":"Babu D. Reddy","year":"2013","journal-title":"Golden Res. Thoughts"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T07:27:56Z","timestamp":1619594876000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500245"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,30]]},"references-count":7,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["10.1142\/S1793830921500245"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500245","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,30]]}}}