{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T12:23:11Z","timestamp":1698582191476},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2011,3]]},"abstract":"<jats:p> Let G = (V, E) be a graph with p vertices and q edges. An acyclic graphoidal cover of G is a collection \u03c8 of paths in G which are internally disjoint and covering each edge of the graph exactly once. Let f : V \u2192 {1, 2, \u2026, p} be a labeling of the vertices of G. Let \u2191G<jats:sub>f<\/jats:sub> be the directed graph obtained by orienting the edges uv of G from u to v provided f(u) &lt; f(v). If the set \u03c8<jats:sub>f<\/jats:sub> of all maximal directed paths in \u2191G<jats:sub>f<\/jats:sub>, with directions ignored, is an acyclic graphoidal cover of G, then f is called a graphoidal labeling of G and G is called a label graphoidal graph and \u03b7<jats:sub>l<\/jats:sub> = min {|\u03c8<jats:sub>f<\/jats:sub>|: f is a graphoidal labeling of G} is called the label graphoidal covering number of G. An orientation of G in which every vertex of degree greater than 2 is either a sink or a source is a graphoidal orientation. In this paper we characterize graphs for which (i) \u03b7<jats:sub>l<\/jats:sub> = \u03b7<jats:sub>a<\/jats:sub> and (ii) \u03b7<jats:sub>l<\/jats:sub> = \u0394. Also, we discuss the relation between graphoidal labeling and graphoidal orientation. <\/jats:p>","DOI":"10.1142\/s179383091100095x","type":"journal-article","created":{"date-parts":[[2011,4,14]],"date-time":"2011-04-14T05:45:47Z","timestamp":1302759947000},"page":"1-7","source":"Crossref","is-referenced-by-count":4,"title":["ON THE LABEL GRAPHOIDAL COVERING NUMBER-II"],"prefix":"10.1142","volume":"03","author":[{"given":"I. SAHUL","family":"HAMID","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Madura College, Madurai, India"}]},{"given":"A.","family":"ANITHA","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Thiagarajar College of Engineering, Madurai, India"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","first-page":"882","volume":"18","author":"Acharya B. D.","journal-title":"Indian J. Pure Appl. Math."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(98)00032-6"},{"key":"rf5","first-page":"#DS6","volume":"5","author":"Gallian J. A.","journal-title":"Electron. J. Combin."},{"key":"rf6","volume-title":"Graph Theory","author":"Harary F.","year":"1972"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179383091100095X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:32:14Z","timestamp":1565127134000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S179383091100095X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":4,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,3]]}},"alternative-id":["10.1142\/S179383091100095X"],"URL":"https:\/\/doi.org\/10.1142\/s179383091100095x","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}