{"id":"https://openalex.org/W2102755079","doi":"https://doi.org/10.1142/s1793830914500608","title":"Some Steiner concepts on lexicographic products of graphs","display_name":"Some Steiner concepts on lexicographic products of graphs","publication_year":2014,"publication_date":"2014-08-19","ids":{"openalex":"https://openalex.org/W2102755079","doi":"https://doi.org/10.1142/s1793830914500608","mag":"2102755079"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830914500608","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500608","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":true,"oa_status":"green","oa_url":"https://dk.um.si/IzpisGradiva.php?id=52006","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075164455","display_name":"Bijo S. Anand","orcid":"https://orcid.org/0000-0002-7221-904X"},"institutions":[{"id":"https://openalex.org/I158338959","display_name":"University of Kerala","ror":"https://ror.org/05tqa9940","country_code":"IN","type":"education","lineage":["https://openalex.org/I158338959"]},{"id":"https://openalex.org/I288496929","display_name":"Narayana Health","ror":"https://ror.org/05kx1ke03","country_code":"IN","type":"healthcare","lineage":["https://openalex.org/I288496929"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Bijo S. Anand","raw_affiliation_strings":["Department of Futures Studies, University of Kerala, Trivandrum-695034, India","Department of Mathematics, Sree Narayana College for Women, Kollam-691001, India"],"affiliations":[{"raw_affiliation_string":"Department of Futures Studies, University of Kerala, Trivandrum-695034, India","institution_ids":["https://openalex.org/I158338959"]},{"raw_affiliation_string":"Department of Mathematics, Sree Narayana College for Women, Kollam-691001, India","institution_ids":["https://openalex.org/I288496929"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074448757","display_name":"Manoj Changat","orcid":"https://orcid.org/0000-0001-7257-6031"},"institutions":[{"id":"https://openalex.org/I158338959","display_name":"University of Kerala","ror":"https://ror.org/05tqa9940","country_code":"IN","type":"education","lineage":["https://openalex.org/I158338959"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Manoj Changat","raw_affiliation_strings":["Department of Futures Studies, University of Kerala, Trivandrum-695581, India"],"affiliations":[{"raw_affiliation_string":"Department of Futures Studies, University of Kerala, Trivandrum-695581, India","institution_ids":["https://openalex.org/I158338959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003861860","display_name":"Iztok Peterin","orcid":"https://orcid.org/0000-0002-1990-6967"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Iztok Peterin","raw_affiliation_strings":["University of Maribor, FEECS, Smetanova 17, 2000 Maribor, Slovenia"],"affiliations":[{"raw_affiliation_string":"University of Maribor, FEECS, Smetanova 17, 2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057486216","display_name":"Prasanth G. Narasimha-Shenoi","orcid":"https://orcid.org/0000-0002-5850-5410"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Prasanth G. Narasimha-Shenoi","raw_affiliation_strings":["Department of Mathematics, Government College, Chittur, Palakkad-678 104, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College, Chittur, Palakkad-678 104, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5075164455"],"corresponding_institution_ids":["https://openalex.org/I158338959","https://openalex.org/I288496929"],"apc_list":null,"apc_paid":null,"fwci":0.3656,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.65599286,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"06","issue":"04","first_page":"1450060","last_page":"1450060"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":1.0,"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":1.0,"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":0.998199999332428,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/steiner-tree-problem","display_name":"Steiner tree problem","score":0.8952441811561584},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8577098846435547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7795302271842957},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.5495251417160034},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48658955097198486},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.46660324931144714},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.45137467980384827},{"id":"https://openalex.org/keywords/steiner-system","display_name":"Steiner system","score":0.4365028738975525}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.8952441811561584},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8577098846435547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7795302271842957},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.5495251417160034},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48658955097198486},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46660324931144714},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.45137467980384827},{"id":"https://openalex.org/C175695255","wikidata":"https://www.wikidata.org/wiki/Q4420916","display_name":"Steiner system","level":2,"score":0.4365028738975525},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s1793830914500608","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500608","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"},{"id":"pmh:oai:dk.um.si:IzpisGradiva.php?id=52006","is_oa":true,"landing_page_url":"https://dk.um.si/IzpisGradiva.php?id=52006","pdf_url":null,"source":{"id":"https://openalex.org/S4377196302","display_name":"University of Maribor digital library (University of Maribor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I37696226","host_organization_name":"University of Maribor","host_organization_lineage":["https://openalex.org/I37696226"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Preprint series, vol. 1179, no. 50, pp. 1-15, 2012.","raw_type":"info:eu-repo/semantics/other"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.417.2627","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.417.2627","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.imfm.si/preprinti/PDF/01179.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:dk.um.si:IzpisGradiva.php?id=52006","is_oa":true,"landing_page_url":"https://dk.um.si/IzpisGradiva.php?id=52006","pdf_url":null,"source":{"id":"https://openalex.org/S4377196302","display_name":"University of Maribor digital library (University of Maribor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I37696226","host_organization_name":"University of Maribor","host_organization_lineage":["https://openalex.org/I37696226"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Preprint series, vol. 1179, no. 50, pp. 1-15, 2012.","raw_type":"info:eu-repo/semantics/other"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W55321067","https://openalex.org/W577570849","https://openalex.org/W1520111182","https://openalex.org/W1967641001","https://openalex.org/W1970115538","https://openalex.org/W1972322699","https://openalex.org/W1983797958","https://openalex.org/W1984989930","https://openalex.org/W1988790243","https://openalex.org/W1994891352","https://openalex.org/W2000027979","https://openalex.org/W2013441256","https://openalex.org/W2016251682","https://openalex.org/W2026338696","https://openalex.org/W2069038356","https://openalex.org/W2070372004","https://openalex.org/W2080743565","https://openalex.org/W2091254185","https://openalex.org/W2102217150","https://openalex.org/W2117475001","https://openalex.org/W2124840911","https://openalex.org/W2127155173","https://openalex.org/W2131690757","https://openalex.org/W2490805901"],"related_works":["https://openalex.org/W2775050868","https://openalex.org/W2897343264","https://openalex.org/W2025658531","https://openalex.org/W2500374022","https://openalex.org/W2003806381","https://openalex.org/W2090486508","https://openalex.org/W2051685615","https://openalex.org/W1991925252","https://openalex.org/W4254035687","https://openalex.org/W2500007129"],"abstract_inverted_index":{"Let":[0],"G":[1],"be":[2],"a":[3,7,26,37,57,74,100],"graph":[4],"and":[5,45,95,99],"W":[6,24,44,55],"subset":[8],"of":[9,17,23,33,35,43,47,63,69],"V(G).":[10],"A":[11],"subtree":[12],"with":[13,81],"the":[14,40,66,78,84,87,90,92,96,104],"minimum":[15],"number":[16,32],"edges":[18,34],"that":[19],"contains":[20],"all":[21,48],"vertices":[22,49],"is":[25,39],"Steiner":[27,41,52,58,85,88],"tree":[28,38],"for":[29,54,65,77,103],"W.":[30],"The":[31],"such":[36],"distance":[42],"union":[46],"belonging":[50],"to":[51,83],"trees":[53],"form":[56],"interval.":[59],"We":[60,71],"describe":[61],"both":[62],"these":[64],"lexicographic":[67],"product":[68],"graphs.":[70],"also":[72],"give":[73],"complete":[75],"answer":[76,102],"following":[79],"invariants":[80],"respect":[82],"convexity:":[86],"number,":[89,94,98],"rank,":[91],"hull":[93],"Carath\u00e9odory":[97],"partial":[101],"Radon":[105],"number.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
