{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T09:51:45Z","timestamp":1649065905464},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p> For a connected graph G = (V, E), a set S<jats:sub>e<\/jats:sub> \u2286 E(G)\u2013{e} is called an edge fixing edge-to-vertex monophonic set of an edge e of a connected graph G if every vertex of G lies on an e \u2013 f edge-to-vertex monophonic path of G, where f \u2208 S<jats:sub>e<\/jats:sub>. The edge fixing edge-to-vertex monophonic number m<jats:sub>efev<\/jats:sub>(G) of G is the minimum cardinality of its edge fixing edge-to-vertex monophonic sets of an edge e of G. A subset M<jats:sub>e<\/jats:sub> \u2286 S<jats:sub>e<\/jats:sub> in a connected graph G is called a forcing subset for S<jats:sub>e<\/jats:sub>, if S<jats:sub>e<\/jats:sub> is the unique edge fixing edge-to-vertex monophonic set of e of G containing M<jats:sub>e<\/jats:sub>. A forcing subset for S<jats:sub>e<\/jats:sub> of minimum cardinality is a minimum subset of S<jats:sub>e<\/jats:sub>. The forcing edge fixing edge-to-vertex monophonic number of G denoted by f<jats:sub>efev<\/jats:sub>(G) = min {f<jats:sub>efev<\/jats:sub>(S<jats:sub>e<\/jats:sub>)}, where the minimum is taken over all cardinality of a minimal edge fixing edge-to-vertex monophonic set of e of G. The forcing edge fixing edge-to-vertex monophonic number of certain classes of graphs is determined and some of its general properties are studied. It is shown that for every integers a and b with 0 \u2264 a \u2264 b, b \u2265 1, there exists a connected graph G such that f<jats:sub>efev<\/jats:sub>(G) = a, m<jats:sub>efev<\/jats:sub>(G) = b. <\/jats:p>","DOI":"10.1142\/s1793830913500341","type":"journal-article","created":{"date-parts":[[2013,9,4]],"date-time":"2013-09-04T01:03:51Z","timestamp":1378256631000},"page":"1350034","source":"Crossref","is-referenced-by-count":0,"title":["THE FORCING EDGE FIXING EDGE-TO-VERTEX MONOPHONIC NUMBER OF A GRAPH"],"prefix":"10.1142","volume":"05","author":[{"given":"J.","family":"JOHN","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College of Engineering, Tirunelveli-627 007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K. UMA","family":"SAMUNDESVARI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Noorul Islam Centre for Higher Education, Kumaracoil-629 175, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,12,3]]},"reference":[{"key":"rf1","volume-title":"Distance in Graphs","author":"Buckley F.","year":"1990"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.08.039"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2006.08.002"},{"key":"rf4","first-page":"722","volume":"3","author":"John J.","journal-title":"Int. J. Math. Archive"},{"key":"rf5","first-page":"349","volume":"2","author":"John J.","journal-title":"South Asian J. Math."},{"key":"rf7","first-page":"29","volume":"3","author":"John J.","journal-title":"Int. J. Math. Trends and Tech."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1206081J"},{"key":"rf9","first-page":"935","volume":"3","author":"John J.","journal-title":"Int. J. Math. Archive"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830913500341","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:13:47Z","timestamp":1565115227000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830913500341"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":8,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2013,12,3]]},"published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.1142\/S1793830913500341"],"URL":"https:\/\/doi.org\/10.1142\/s1793830913500341","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12]]}}}