{"id":"https://openalex.org/W1972602069","doi":"https://doi.org/10.1142/s1793830912500292","title":"EXTREME STEINER GRAPHS","display_name":"EXTREME STEINER GRAPHS","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W1972602069","doi":"https://doi.org/10.1142/s1793830912500292","mag":"1972602069"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830912500292","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500292","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048977724","display_name":"A. P. Santhakumaran","orcid":null},"institutions":[{"id":"https://openalex.org/I4401726862","display_name":"St. Xavier's College (Autonomous)","ror":"https://ror.org/0316y5a96","country_code":null,"type":"education","lineage":["https://openalex.org/I4401726862"]},{"id":"https://openalex.org/I906608882","display_name":"St Xavier\u2019s College","ror":"https://ror.org/039543c28","country_code":"IN","type":"education","lineage":["https://openalex.org/I906608882"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"A. P. SANTHAKUMARAN","raw_affiliation_strings":["Research Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai - 627 002, India"],"affiliations":[{"raw_affiliation_string":"Research Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai - 627 002, India","institution_ids":["https://openalex.org/I906608882","https://openalex.org/I4401726862"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048977724"],"corresponding_institution_ids":["https://openalex.org/I4401726862","https://openalex.org/I906608882"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.06181358,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"04","issue":"02","first_page":"1250029","last_page":"1250029"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9060980081558228},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.8074987530708313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7736363410949707},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7108784914016724},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.5641130208969116},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4682976305484772},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4651869833469391},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.44459232687950134},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.4282560646533966}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9060980081558228},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.8074987530708313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7736363410949707},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7108784914016724},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.5641130208969116},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4682976305484772},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4651869833469391},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.44459232687950134},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.4282560646533966},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830912500292","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500292","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1574174057","https://openalex.org/W1970115538","https://openalex.org/W1989512718","https://openalex.org/W2014251935","https://openalex.org/W2038715674","https://openalex.org/W2169204877","https://openalex.org/W4213214460"],"related_works":["https://openalex.org/W2937242299","https://openalex.org/W3127652808","https://openalex.org/W2794522194","https://openalex.org/W4283726592","https://openalex.org/W1885115167","https://openalex.org/W2963404550","https://openalex.org/W30750922","https://openalex.org/W3118953946","https://openalex.org/W2994748110","https://openalex.org/W2424154501"],"abstract_inverted_index":{"For":[0,258,293],"a":[1,11,16,23,33,65,96,108,122,153,167,242,350,356,369,395,408],"connected":[2],"graph":[3,168,193,199,209,282,325,364,403],"G":[4,21,50,69,79,106,118,136,169,185,194,283,326,365,404],"of":[5,35,46,78,84,92,100,105,111,117,127,129,135,141,149,157,166,181,218,237,255,284,327,345,390],"order":[6,37,189,219,250,328],"p":[7,220,224,309,311],"\u2265":[8,265,318],"2":[9,266,300,305,317],"and":[10,88,145,205,251,263,289,297,310,332,353,370,409],"set":[12,43,62,67,91,99,104,109,148,156],"W":[13,29,39,63],"\u2286":[14,40],"V(G),":[15],"tree":[17,25,34,56],"T":[18,31],"contained":[19,120],"in":[20,49,121,184],"is":[22,32,64,80,95,107,119,137,152,162,177,186,195,230,245,274,337,375,382,414],"Steiner":[24,55,66,75,86,90,98,198,216,222,252,281,290,324,333,363,418],"with":[26,38,57,221,239,267,299,347,366,392,405],"respect":[27,58],"to":[28,59],"if":[30,70,170,200,210],"minimum":[36,82,97,139,154],"V(T).":[41],"The":[42,61,74,131,179],"S(W)":[44,71],"consists":[45],"all":[47],"vertices":[48,112,128,183],"that":[51,114,232,276,339,374,384,413],"lie":[52],"on":[53],"some":[54,125,256],"W.":[60],"for":[68,340,385],"=":[72,202,212,355,368,372,407,411],"V(G).":[73],"number":[76,133,180,223,291,334],"s(G)":[77,94,201,367,410],"the":[81,138,171,248],"cardinality":[83,93,140,150],"its":[85,142,175,187],"sets":[87,144],"any":[89,146],"G.":[101,158],"A":[102,159,192],"geodetic":[103,132,143,147,155],"S":[110],"such":[113],"every":[115,233,341,386],"vertex":[116,160,165],"geodesic":[123,208,379,402],"joining":[124],"pair":[126,234,342,387],"S.":[130],"g(G)":[134,151,211,371,406],"v":[161],"an":[163,196,206,279,322,361,377,400,416],"extreme":[164,182,188,197,207,249,280,323,362,378,401,417],"subgraph":[172],"induced":[173],"by":[174],"neighbors":[176],"complete.":[178],"ex":[190,203,213],"(G).":[191,214],"(G),":[204],"Extreme":[215],"graphs":[217],"-":[225,312,314],"1":[226],"are":[227],"characterized.":[228],"It":[229,336,381],"shown":[231,275,338,383],"a,":[235,343,388],"b":[236,244,344,352,354,373,389,412],"integers":[238,260,294,346,391],"0":[240],"\u2264":[241,243,271,301,306,349,394],"realizable":[246],"as":[247],"number,":[253],"respectively,":[254],"graph.":[257,380,419],"positive":[259],"r,":[261,286],"d":[262,270,296,302,313,331],"l":[264],"r":[268],"<":[269,303,308,351,396],"2r,":[272],"it":[273],"there":[277,320,359,398],"exists":[278,321,360,399],"radius":[285],"diameter":[287,330],"d,":[288],"l.":[292],"p,":[295,304,329],"k":[298,307,315],"+":[316,357],"0,":[319],"k.":[335],"3":[348,393],"1,":[358],"not":[376,415],"b,":[397]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}