{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T05:23:31Z","timestamp":1648877011253},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2015,6]]},"abstract":"<jats:p> For a graph G = (V, E) and a nonempty set X, a linear hypergraph set-indexer (LHSI) is a function f : V(G) \u2192 2<jats:sup>X<\/jats:sup> satisfying the following conditions: (i) f is injective (ii) the ordered pair H<jats:sub>f<\/jats:sub>(G) = (X, f(V)), where f(V) = {f(v) : v \u2208 V(G)}, is a linear hypergraph (iii) the induced function f<jats:sup>\u2295<\/jats:sup> : E \u2192 2<jats:sup>X<\/jats:sup> defined by f<jats:sup>\u2295<\/jats:sup>(uv) = f(u) \u2295 f(v), for all uv \u2208 E is injective and (iv) H<jats:sub>f<jats:sup>\u2295<\/jats:sup><\/jats:sub>(G) = (X, f<jats:sup>\u2295<\/jats:sup>(E)), where f<jats:sup>\u2295<\/jats:sup>(E) = {f<jats:sup>\u2295<\/jats:sup>(e) : e \u2208 E}, is a linear hypergraph. It is shown that a 3-uniform LHSI of a graph, corresponding to upper LHSI number, is unique up to isomorphism and possible relations between the coloring numbers of a given graph and the two linear set-indexing hypergraphs are established. Also, we show that the two hypergraphs associated with an extremal 3-uniform LHSI of a graph are 2-colorable and the corresponding induced edge hypergraphs are self-dual. <\/jats:p>","DOI":"10.1142\/s1793830915500159","type":"journal-article","created":{"date-parts":[[2015,2,26]],"date-time":"2015-02-26T02:58:56Z","timestamp":1424919536000},"page":"1550015","source":"Crossref","is-referenced-by-count":0,"title":["On hypergraph coloring and 3-uniform linear hypergraph set-indexers of a graph"],"prefix":"10.1142","volume":"07","author":[{"given":"Viji","family":"Paul","sequence":"first","affiliation":[{"name":"Department of Mathematics, WMO Arts and Science College, Muttil, Kerala, India"}]},{"given":"K A","family":"Germina","sequence":"additional","affiliation":[{"name":"Research Centre and PG Department of Mathematics, Mary Matha Arts and Science College, Vemom P.O., Mananthavady 670645, India"}]}],"member":"219","published-online":{"date-parts":[[2015,5,25]]},"reference":[{"key":"rf1","series-title":"MRI Lecture Notes in Applied Mathematics","volume-title":"Set-valuations of Graphs and Their Applications","author":"Acharya B. D.","year":"1983"},{"key":"rf2","first-page":"3359","volume":"5","author":"Acharya B. D.","year":"2010","journal-title":"Int. Math. Forum"},{"key":"rf3","first-page":"425","volume":"3","author":"Alon N.","year":"1996","journal-title":"Nordic J. Comput."},{"key":"rf7","first-page":"861","volume":"6","author":"Paul V.","year":"2011","journal-title":"Int. J. Contemp. Math. Sci."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/25.1.303"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1992-1135027-1"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830915500159","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:36:03Z","timestamp":1565148963000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830915500159"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,25]]},"references-count":6,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2015,5,25]]},"published-print":{"date-parts":[[2015,6]]}},"alternative-id":["10.1142\/S1793830915500159"],"URL":"https:\/\/doi.org\/10.1142\/s1793830915500159","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,25]]}}}