{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:36:09Z","timestamp":1759638969981},"reference-count":24,"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>The metric dimension of a graph G, denoted by dim (G), is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let G<jats:sub>1<\/jats:sub>and G<jats:sub>2<\/jats:sub>be disjoint copies of a graph G and let f : V(G<jats:sub>1<\/jats:sub>) \u2192 V(G<jats:sub>2<\/jats:sub>) be a function. Then a functigraphC(G, f) = (V, E) has the vertex set V = V(G<jats:sub>1<\/jats:sub>) \u222a V(G<jats:sub>2<\/jats:sub>) and the edge set E = E(G<jats:sub>1<\/jats:sub>) \u222a E(G<jats:sub>2<\/jats:sub>) \u222a {uv | v = f(u)}. We study how metric dimension behaves in passing from G to C(G, f) by first showing that 2 \u2264 dim (C(G, f)) \u2264 2n - 3, if G is a connected graph of order n \u2265 3 and f is any function. We further investigate the metric dimension of functigraphs on complete graphs and on cycles.<\/jats:p>","DOI":"10.1142\/s1793830912500607","type":"journal-article","created":{"date-parts":[[2013,12,3]],"date-time":"2013-12-03T09:56:07Z","timestamp":1386064567000},"page":"1250060","source":"Crossref","is-referenced-by-count":3,"title":["ON METRIC DIMENSION OF FUNCTIGRAPHS"],"prefix":"10.1142","volume":"05","author":[{"given":"LINDA","family":"EROH","sequence":"first","affiliation":[{"name":"University of Wisconsin Oshkosh, Oshkosh, WI 54901, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CONG X.","family":"KANG","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University at Galveston, Galveston, TX 77553, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EUNJEONG","family":"YI","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University at Galveston, Galveston, TX 77553, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,12,3]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdq096"},{"key":"rf2","first-page":"97","volume":"13","author":"Bailey R. F.","journal-title":"Discrete Math. Theor. Comput. Sci."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025745406160"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/050641867"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00198-0"},{"key":"rf6","first-page":"433","volume":"3","author":"Chartrand G.","journal-title":"Ann. Inst. H. Poincare (Sect. B)"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(00)00126-7"},{"key":"rf8","first-page":"47","volume":"160","author":"Chartrand G.","journal-title":"Congr. Numer."},{"key":"rf9","volume-title":"Introduction to Graph Theory","author":"Chartrand G.","year":"2004"},{"key":"rf10","doi-asserted-by":"crossref","first-page":"27","DOI":"10.21136\/MB.2011.141447","volume":"136","author":"Chen A.","journal-title":"Math. Bohem."},{"key":"rf11","first-page":"277","volume":"28","author":"D\u00f6rfler W.","journal-title":"Math. Solvaca"},{"key":"rf12","first-page":"193","volume":"83","author":"Eroh L.","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.11.020"},{"key":"rf14","volume-title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","author":"Garey M. R.","year":"1979"},{"key":"rf15","author":"Guo J.","journal-title":"J. Comb. Optim."},{"key":"rf16","first-page":"191","volume":"2","author":"Harary F.","journal-title":"Ars Combin."},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0060115"},{"key":"rf18","volume":"17","author":"Hernando C.","journal-title":"Electron. J. Combin."},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(95)00106-2"},{"key":"rf20","first-page":"17","volume":"40","author":"Poisson C.","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1030.0070"},{"key":"rf22","first-page":"217","volume":"8","author":"Shanmukha B.","journal-title":"Far East J. Appl. Math."},{"key":"rf23","first-page":"549","volume":"14","author":"Slater P. J.","journal-title":"Congr. Numer."},{"key":"rf24","first-page":"445","volume":"22","author":"Slater P. J.","journal-title":"J. Math. Phys. Sci."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500607","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,11]],"date-time":"2020-08-11T07:28:02Z","timestamp":1597130882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500607"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":24,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2013,12,3]]},"published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.1142\/S1793830912500607"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500607","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12]]}}}