{"id":"https://openalex.org/W1972150661","doi":"https://doi.org/10.1002/net.3230180302","title":"On graphs with signed inverses","display_name":"On graphs with signed inverses","publication_year":1988,"publication_date":"1988-09-01","ids":{"openalex":"https://openalex.org/W1972150661","doi":"https://doi.org/10.1002/net.3230180302","mag":"1972150661"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230180302","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230180302","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5048753010","display_name":"Fred Buckley","orcid":null},"institutions":[{"id":"https://openalex.org/I141810926","display_name":"Baruch College","ror":"https://ror.org/023qavy03","country_code":"US","type":"education","lineage":["https://openalex.org/I141810926"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Fred Buckley","raw_affiliation_strings":["Mathematics Department, Baruch College (CUNY), New York, New York 10010","Mathematics Department Baruch College, Cuny New York, New York 10010"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Baruch College (CUNY), New York, New York 10010","institution_ids":["https://openalex.org/I141810926"]},{"raw_affiliation_string":"Mathematics Department Baruch College, Cuny New York, New York 10010","institution_ids":["https://openalex.org/I141810926"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028422739","display_name":"Lynne L. Doty","orcid":null},"institutions":[{"id":"https://openalex.org/I926137907","display_name":"Marist College","ror":"https://ror.org/04wx3x242","country_code":"US","type":"education","lineage":["https://openalex.org/I926137907"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lynne L. Doty","raw_affiliation_strings":["Division of Computer Science and Mathematics, Marist College, Poughkeepsie, New York 12601"],"affiliations":[{"raw_affiliation_string":"Division of Computer Science and Mathematics, Marist College, Poughkeepsie, New York 12601","institution_ids":["https://openalex.org/I926137907"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111801246","display_name":"Frank Harary","orcid":null},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Frank Harary","raw_affiliation_strings":["Department of Mathematical Sciences and of Computer Science, New Mexico State University, Las Cruces, New Mexico 88003"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences and of Computer Science, New Mexico State University, Las Cruces, New Mexico 88003","institution_ids":["https://openalex.org/I10052268"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048753010"],"corresponding_institution_ids":["https://openalex.org/I141810926"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.08595327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"3","first_page":"151","last_page":"157"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","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/T11797","display_name":"graph theory and CDMA systems","score":0.9818000197410583,"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/invertible-matrix","display_name":"Invertible matrix","score":0.8604139089584351},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7261635661125183},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.7026023864746094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6395688056945801},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5063694715499878},{"id":"https://openalex.org/keywords/signed-graph","display_name":"Signed graph","score":0.4971344769001007},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4931785464286804},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4511772692203522},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11073100566864014}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.8604139089584351},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7261635661125183},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.7026023864746094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6395688056945801},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5063694715499878},{"id":"https://openalex.org/C2779773260","wikidata":"https://www.wikidata.org/wiki/Q11246292","display_name":"Signed graph","level":3,"score":0.4971344769001007},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4931785464286804},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4511772692203522},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11073100566864014},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230180302","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230180302","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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":5,"referenced_works":["https://openalex.org/W1980769375","https://openalex.org/W1985911376","https://openalex.org/W2333403316","https://openalex.org/W4213214460","https://openalex.org/W4249011881"],"related_works":["https://openalex.org/W1996208176","https://openalex.org/W2981681393","https://openalex.org/W4220926261","https://openalex.org/W3200633635","https://openalex.org/W2886125143","https://openalex.org/W1577070942","https://openalex.org/W4248988865","https://openalex.org/W4289703793","https://openalex.org/W2022287750","https://openalex.org/W4362607598"],"abstract_inverted_index":{"Abstract":[0],"A":[1,11],"graph":[2,22,80],"G":[3,49],"is":[4,16,55],"called":[5],"invertible":[6,44],"if":[7],"its":[8],"adjacency":[9,18],"matrix":[10,19],"has":[12],"an":[13],"inverse":[14,53],"which":[15],"the":[17,35,67,76],"of":[20,64,72,78],"some":[21],"H.":[23],"All":[24],"such":[25],"graphs":[26,48],"were":[27],"shown":[28],"by":[29],"Harary":[30],"and":[31,75],"Minc":[32],"to":[33],"have":[34],"form":[36],"nK":[37],"2":[38,70],".":[39,84],"We":[40,59,85],"now":[41],"introduce":[42],"signed":[43,57],"(or":[45],"briefly":[46],"s\u2010invertible)":[47],"as":[50],"those":[51],"whose":[52],"H":[54],"a":[56],"graph.":[58],"identify":[60],"two":[61],"infinite":[62],"classes":[63],"s\u2010invertible":[65,88],"graphs:":[66],"paths":[68],"P":[69],"n":[71],"even":[73],"order,":[74],"corona":[77],"any":[79],"with":[81],"K":[82],"1":[83],"then":[86],"characterize":[87],"trees.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}