{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,16]],"date-time":"2024-03-16T07:40:17Z","timestamp":1710574817386},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,8]]},"abstract":"<jats:p>Hedrl\u00edn and Pultr proved that for any monoid M there exists a graph G with endomorphism monoid isomorphic to M. In a previous paper, we give a construction G(M) for a graph with prescribed endomorphism monoid M known as a [Formula: see text]-graph. Using this construction, we derived bounds on the minimum number of vertices and edges required to produce a graph with a given endomorphism monoid for various classes of finite monoids. In this paper, we generalize the [Formula: see text]-graph construction and derive several new bounds for monoid classes not handled by our first paper. Among these are the so called \"strong semilattices of C-semigroups\" where C is one of the following: Groups, Abelian Groups, Rectangular Groups, and completely simple semigroups.<\/jats:p>","DOI":"10.1142\/s0218196709005275","type":"journal-article","created":{"date-parts":[[2009,9,3]],"date-time":"2009-09-03T11:03:24Z","timestamp":1251975804000},"page":"705-721","source":"Crossref","is-referenced-by-count":1,"title":["REPRESENTING SUBDIRECT PRODUCT MONOIDS BY GRAPHS"],"prefix":"10.1142","volume":"19","author":[{"given":"V\u00c1CLAV","family":"KOUBEK","sequence":"first","affiliation":[{"name":"Department of Theoretical Comp. Sci and Math. Logic, The Faculty of Mathematics and Physics, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic"}]},{"given":"VOJT\u011aCH","family":"R\u00d6DL","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Emory University, Atlanta, USA"}]},{"given":"BENJAMIN","family":"SHEMMER","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Emory University, Atlanta, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01360726"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1974-082-9"},{"key":"rf4","first-page":"239","volume":"6","author":"Frucht R.","journal-title":"Compos. Math."},{"key":"rf5","volume-title":"Abelian Groups","author":"Fuchs L.","year":"1960"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1971.39.669"},{"key":"rf7","first-page":"161","volume":"4","author":"Hedrl\u00edn Z.","journal-title":"Comment. Math. Univ. Carolinae"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01298508"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01297617"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1970-071-3"},{"key":"rf11","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198535775.001.0001","volume-title":"Techniques of Semigroup Theory","author":"Higgins P. M.","year":"1992"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(84)90021-2"},{"key":"rf13","author":"Koubek V.","journal-title":"J. Graph Theory"},{"key":"rf14","volume-title":"Introduction to Semigroups","author":"Petrich M.","year":"1973"},{"key":"rf15","series-title":"North-Holland Mathematical Library","volume-title":"Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories","author":"Pultr A.","year":"1980"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005275","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,16]],"date-time":"2024-03-16T07:25:36Z","timestamp":1710573936000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005275"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8]]},"references-count":14,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,8]]}},"alternative-id":["10.1142\/S0218196709005275"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005275","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8]]}}}