{"id":"https://openalex.org/W1600737180","doi":"https://doi.org/10.37236/626","title":"Uniqueness of Graph Square Roots of Girth Six","display_name":"Uniqueness of Graph Square Roots of Girth Six","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W1600737180","doi":"https://doi.org/10.37236/626","mag":"1600737180"},"language":"en","primary_location":{"id":"doi:10.37236/626","is_oa":true,"landing_page_url":"https://doi.org/10.37236/626","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p139/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p139/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050123676","display_name":"Anna Adamaszek","orcid":"https://orcid.org/0000-0003-3291-0124"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Anna Adamaszek","raw_affiliation_strings":["University of Warsaw"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warsaw","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085411159","display_name":"Micha\u0142 Adamaszek","orcid":"https://orcid.org/0000-0003-3551-192X"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Micha\u0142 Adamaszek","raw_affiliation_strings":["University of Warsaw"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warsaw","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6091,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.88715583,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9987999796867371,"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/T11797","display_name":"graph theory and CDMA systems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9290239810943604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8268749713897705},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.6934516429901123},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5808666348457336},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4838506281375885},{"id":"https://openalex.org/keywords/odd-graph","display_name":"Odd graph","score":0.4798373878002167},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4636024236679077},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4574548304080963},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.3552874028682709},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.2057659924030304}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9290239810943604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8268749713897705},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.6934516429901123},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5808666348457336},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4838506281375885},{"id":"https://openalex.org/C206815938","wikidata":"https://www.wikidata.org/wiki/Q7077445","display_name":"Odd graph","level":5,"score":0.4798373878002167},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4636024236679077},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4574548304080963},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.3552874028682709},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.2057659924030304},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/626","is_oa":true,"landing_page_url":"https://doi.org/10.37236/626","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p139/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.661.7464","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.661.7464","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"http://wrap.warwick.ac.uk/38719/1/WRAP_Adamaszek_Uniqueness_graph_square.pdf","raw_type":"text"},{"id":"pmh:oai:wrap.warwick.ac.uk:38719","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.6230","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.6230","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v18i1p139/pdf/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.745.6102","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.745.6102","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0912.2291.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/626","is_oa":true,"landing_page_url":"https://doi.org/10.37236/626","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p139/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6958986694","display_name":null,"funder_award_id":"EP/D063191/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7410676224","display_name":"The Centre for Discrete Mathematics and its Applications (DIMAP)","funder_award_id":"EP/D063191/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1600737180.pdf","grobid_xml":"https://content.openalex.org/works/W1600737180.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1711880449","https://openalex.org/W1979064908","https://openalex.org/W1995432558","https://openalex.org/W2044570479"],"related_works":["https://openalex.org/W2552197458","https://openalex.org/W2963883188","https://openalex.org/W2473857262","https://openalex.org/W2135056220","https://openalex.org/W2345067526","https://openalex.org/W2073879033","https://openalex.org/W4254914975","https://openalex.org/W1991809067","https://openalex.org/W4232305414","https://openalex.org/W2077949955"],"abstract_inverted_index":{"We":[0,49],"prove":[1],"that":[2],"if":[3],"two":[4],"graphs":[5,16,43,57],"of":[6,26,29,38,44,56],"girth":[7,45],"at":[8,46],"least":[9,47],"$6$":[10],"have":[11],"isomorphic":[12],"squares,":[13],"then":[14],"the":[15,22,27,36],"themselves":[17],"are":[18],"isomorphic.":[19],"This":[20],"is":[21],"best":[23],"possible":[24],"extension":[25],"results":[28,37],"Ross":[30],"and":[31,35],"Harary":[32],"on":[33,42,54],"trees":[34],"Farzad":[39],"et":[40],"al.":[41],"$7$.":[48],"also":[50],"make":[51],"a":[52],"remark":[53],"reconstruction":[55],"from":[58],"their":[59],"higher":[60],"powers.":[61]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
