{"id":"https://openalex.org/W2052849659","doi":"https://doi.org/10.1007/s00373-012-1177-8","title":"Planar Lattice Graphs with Gallai\u2019s Property","display_name":"Planar Lattice Graphs with Gallai\u2019s Property","publication_year":2012,"publication_date":"2012-05-03","ids":{"openalex":"https://openalex.org/W2052849659","doi":"https://doi.org/10.1007/s00373-012-1177-8","mag":"2052849659"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-012-1177-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-012-1177-8","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","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/A5038635703","display_name":"Muhammad Faisal Nadeem","orcid":"https://orcid.org/0000-0002-3175-7191"},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Faisal Nadeem","raw_affiliation_strings":["Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020468332","display_name":"Ayesha Shabbir","orcid":"https://orcid.org/0000-0002-3392-7166"},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Ayesha Shabbir","raw_affiliation_strings":["Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050057586","display_name":"Tudor Zamfirescu","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]},{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["DE","PK","RO"],"is_corresponding":true,"raw_author_name":"Tudor Zamfirescu","raw_affiliation_strings":["Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan","Faculty of Mathematics, University of Dortmund, 44221, Dortmund, Germany","Institute of Mathematics, Roumanian Academy, Bucharest, Roumania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan","institution_ids":["https://openalex.org/I43879129"]},{"raw_affiliation_string":"Faculty of Mathematics, University of Dortmund, 44221, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Institute of Mathematics, Roumanian Academy, Bucharest, Roumania","institution_ids":["https://openalex.org/I58077936"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050057586"],"corresponding_institution_ids":["https://openalex.org/I200332995","https://openalex.org/I43879129","https://openalex.org/I58077936"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":2.5892,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.9002482,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"5","first_page":"1523","last_page":"1529"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9952999949455261,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9952999949455261,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9905999898910522,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9779000282287598,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7919937372207642},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6999857425689697},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5929437875747681},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4794263243675232},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.4593006372451782},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.45755138993263245},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4572649896144867},{"id":"https://openalex.org/keywords/square-tiling","display_name":"Square tiling","score":0.4365713596343994},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.4268140494823456},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.42054033279418945},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.39476728439331055},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3526427745819092},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.2880675792694092},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.16324689984321594},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05857780575752258}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7919937372207642},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6999857425689697},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5929437875747681},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4794263243675232},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.4593006372451782},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.45755138993263245},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4572649896144867},{"id":"https://openalex.org/C178650486","wikidata":"https://www.wikidata.org/wiki/Q1128619","display_name":"Square tiling","level":3,"score":0.4365713596343994},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.4268140494823456},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.42054033279418945},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.39476728439331055},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3526427745819092},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.2880675792694092},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.16324689984321594},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05857780575752258},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-012-1177-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-012-1177-8","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323444","display_name":"Autoritatea National\u0103 pentru Cercetare Stiintific\u0103","ror":"https://ror.org/03padf885"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W571298146","https://openalex.org/W1445087869","https://openalex.org/W1964033469","https://openalex.org/W1998311500","https://openalex.org/W2016117822","https://openalex.org/W2021292985","https://openalex.org/W2060445610","https://openalex.org/W2062131958","https://openalex.org/W2162263336","https://openalex.org/W2531095544","https://openalex.org/W4244752224"],"related_works":["https://openalex.org/W3130332934","https://openalex.org/W603403972","https://openalex.org/W4361825306","https://openalex.org/W2031276298","https://openalex.org/W2093949146","https://openalex.org/W2367177042","https://openalex.org/W1560307591","https://openalex.org/W2029854525","https://openalex.org/W2133160845","https://openalex.org/W4386528600"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}