{"id":"https://openalex.org/W2131259888","doi":"https://doi.org/10.26493/1855-3974.245.348","title":"Distinguishing numbers of Cartesian products of multiple complete graphs","display_name":"Distinguishing numbers of Cartesian products of multiple complete graphs","publication_year":2012,"publication_date":"2012-02-01","ids":{"openalex":"https://openalex.org/W2131259888","doi":"https://doi.org/10.26493/1855-3974.245.348","mag":"2131259888"},"language":"en","primary_location":{"id":"doi:10.26493/1855-3974.245.348","is_oa":true,"landing_page_url":"https://doi.org/10.26493/1855-3974.245.348","pdf_url":"https://amc-journal.eu/index.php/amc/article/download/245/160","source":{"id":"https://openalex.org/S61442588","display_name":"Ars Mathematica Contemporanea","issn_l":"1855-3966","issn":["1855-3966","1855-3974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310314472","host_organization_name":"Society of Mathematicians, Physicists and Astronomers of Slovenia","host_organization_lineage":["https://openalex.org/P4310314472"],"host_organization_lineage_names":["Society of Mathematicians, Physicists and Astronomers of Slovenia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Mathematica Contemporanea","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://amc-journal.eu/index.php/amc/article/download/245/160","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001103942","display_name":"Michael Fisher","orcid":"https://orcid.org/0000-0003-0218-3069"},"institutions":[{"id":"https://openalex.org/I161171246","display_name":"West Chester University","ror":"https://ror.org/0053n5071","country_code":"US","type":"education","lineage":["https://openalex.org/I161171246"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael J. Fisher","raw_affiliation_strings":["West Chester University"],"affiliations":[{"raw_affiliation_string":"West Chester University","institution_ids":["https://openalex.org/I161171246"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066177775","display_name":"Garth Isaak","orcid":null},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Garth Isaak","raw_affiliation_strings":["Lehigh University","Lehigh University,"],"affiliations":[{"raw_affiliation_string":"Lehigh University","institution_ids":["https://openalex.org/I186143895"]},{"raw_affiliation_string":"Lehigh University,","institution_ids":["https://openalex.org/I186143895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001103942"],"corresponding_institution_ids":["https://openalex.org/I161171246"],"apc_list":null,"apc_paid":null,"fwci":1.0384,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.78733655,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":"1","first_page":"159","last_page":"173"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998999834060669,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998999834060669,"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/T11708","display_name":"Photochromic and Fluorescence Chemistry","score":0.9674999713897705,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.9735147953033447},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8492348194122314},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7553098201751709},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.6109218597412109},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.590036153793335},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4094370901584625},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1007390022277832}],"concepts":[{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.9735147953033447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8492348194122314},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7553098201751709},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.6109218597412109},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.590036153793335},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4094370901584625},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1007390022277832}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.26493/1855-3974.245.348","is_oa":true,"landing_page_url":"https://doi.org/10.26493/1855-3974.245.348","pdf_url":"https://amc-journal.eu/index.php/amc/article/download/245/160","source":{"id":"https://openalex.org/S61442588","display_name":"Ars Mathematica Contemporanea","issn_l":"1855-3966","issn":["1855-3966","1855-3974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310314472","host_organization_name":"Society of Mathematicians, Physicists and Astronomers of Slovenia","host_organization_lineage":["https://openalex.org/P4310314472"],"host_organization_lineage_names":["Society of Mathematicians, Physicists and Astronomers of Slovenia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Mathematica Contemporanea","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.636.4093","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.636.4093","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lehigh.edu/~gi02/AMC2012.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.26493/1855-3974.245.348","is_oa":true,"landing_page_url":"https://doi.org/10.26493/1855-3974.245.348","pdf_url":"https://amc-journal.eu/index.php/amc/article/download/245/160","source":{"id":"https://openalex.org/S61442588","display_name":"Ars Mathematica Contemporanea","issn_l":"1855-3966","issn":["1855-3966","1855-3974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310314472","host_organization_name":"Society of Mathematicians, Physicists and Astronomers of Slovenia","host_organization_lineage":["https://openalex.org/P4310314472"],"host_organization_lineage_names":["Society of Mathematicians, Physicists and Astronomers of Slovenia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Mathematica Contemporanea","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2131259888.pdf","grobid_xml":"https://content.openalex.org/works/W2131259888.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1855706715","https://openalex.org/W1983094982","https://openalex.org/W1988011615","https://openalex.org/W2003755322","https://openalex.org/W2012186425","https://openalex.org/W2045398969","https://openalex.org/W2081088856","https://openalex.org/W2116983645","https://openalex.org/W3000034718","https://openalex.org/W4205407115","https://openalex.org/W6602136736"],"related_works":["https://openalex.org/W2949097972","https://openalex.org/W4299640900","https://openalex.org/W2141418112","https://openalex.org/W3163064202","https://openalex.org/W2738565459","https://openalex.org/W3159629589","https://openalex.org/W3030274415","https://openalex.org/W68628300","https://openalex.org/W2805104459","https://openalex.org/W2804776333"],"abstract_inverted_index":{"We":[0,16],"examine":[1],"the":[2,6,27,31],"distinguishing":[3,28],"number":[4,12,29],"of":[5,9,13,30,34,37,74],"Cartesian":[7,32],"product":[8,33],"an":[10],"arbitrary":[11],"complete":[14,35],"graphs.":[15],"show":[17],"that":[18],"for":[19],"u":[20,25,43,50,67],"1":[21,56,63,66],"\u2264":[22,24],"...":[23],"d":[26,44,51,64],"graphs":[36],"these":[38,75],"sizes":[39],"is":[40,78],"either":[41],"\u2308":[42,49],"1/":[45,52],"s":[46,53,58],"\u2309":[47,54],"or":[48],"+":[55],"where":[57],"=":[59,62],"\u03a0":[60],"i":[61,68],"\u2212":[65],".":[69],"In":[70],"most":[71],"cases,":[72],"which":[73],"values":[76],"it":[77],"can":[79],"be":[80],"explicitly":[81],"determined.":[82]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}