{"id":"https://openalex.org/W2097211749","doi":"https://doi.org/10.1080/00207169708804573","title":"On complete systems of invariants for small graphs","display_name":"On complete systems of invariants for small graphs","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2097211749","doi":"https://doi.org/10.1080/00207169708804573","mag":"2097211749"},"language":"en","primary_location":{"id":"doi:10.1080/00207169708804573","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804573","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/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 Computer Science, New Mexico State University, Las Cruces, New Mexico, 88003, USA","Department of Computer Science, New Mexico State University, Las Cruces, New Mexico 88003, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, New Mexico State University, Las Cruces, New Mexico, 88003, USA","institution_ids":["https://openalex.org/I10052268"]},{"raw_affiliation_string":"Department of Computer Science, New Mexico State University, Las Cruces, New Mexico 88003, USA","institution_ids":["https://openalex.org/I10052268"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080071481","display_name":"Stavros D. Nikolopoulos","orcid":"https://orcid.org/0000-0001-6684-8459"},"institutions":[{"id":"https://openalex.org/I34771391","display_name":"University of Cyprus","ror":"https://ror.org/02qjrjx09","country_code":"CY","type":"education","lineage":["https://openalex.org/I34771391"]}],"countries":["CY"],"is_corresponding":false,"raw_author_name":"Stavros D. Nikolopoulos","raw_affiliation_strings":["Department of Computer Science, University of Cyprus, CY, Nicosia, 1789, Cyprus","Department of Computer Science , University of Cyprus , CY, Nicosia, 1789, Cyprus"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Cyprus, CY, Nicosia, 1789, Cyprus","institution_ids":["https://openalex.org/I34771391"]},{"raw_affiliation_string":"Department of Computer Science , University of Cyprus , CY, Nicosia, 1789, Cyprus","institution_ids":["https://openalex.org/I34771391"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.23528815,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"1-2","first_page":"35","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9987000226974487,"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"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9980000257492065,"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/graph-isomorphism","display_name":"Graph isomorphism","score":0.7124334573745728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6656669974327087},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6607998609542847},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6465719938278198},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.6293495893478394},{"id":"https://openalex.org/keywords/graph-homomorphism","display_name":"Graph homomorphism","score":0.5271788835525513},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5112171173095703},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.4759390354156494},{"id":"https://openalex.org/keywords/graph-property","display_name":"Graph property","score":0.45249268412590027},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.4514455497264862},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4432021975517273},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.41175219416618347},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.25100117921829224}],"concepts":[{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.7124334573745728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6656669974327087},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6607998609542847},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6465719938278198},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6293495893478394},{"id":"https://openalex.org/C7036158","wikidata":"https://www.wikidata.org/wiki/Q3385162","display_name":"Graph homomorphism","level":5,"score":0.5271788835525513},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5112171173095703},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.4759390354156494},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.45249268412590027},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.4514455497264862},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4432021975517273},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.41175219416618347},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.25100117921829224},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169708804573","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804573","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1560182867","https://openalex.org/W1989114462","https://openalex.org/W2015781464","https://openalex.org/W2018480107","https://openalex.org/W2029489043","https://openalex.org/W2073067110","https://openalex.org/W2075442878","https://openalex.org/W2334513187","https://openalex.org/W2494517118","https://openalex.org/W2799004609","https://openalex.org/W2890747390","https://openalex.org/W3005944782","https://openalex.org/W3041685368","https://openalex.org/W4205898702","https://openalex.org/W4213214460"],"related_works":["https://openalex.org/W3200877167","https://openalex.org/W3202093591","https://openalex.org/W4389544142","https://openalex.org/W1589992348","https://openalex.org/W2384112252","https://openalex.org/W1988965627","https://openalex.org/W1900138702","https://openalex.org/W1976617626","https://openalex.org/W4245682093","https://openalex.org/W167435155"],"abstract_inverted_index":{"We":[0,87],"define":[1],"a":[2,34,66,109],"small":[3,99],"graph":[4,42,58,110],"to":[5,57,94,119],"be":[6],"one":[7,41],"with":[8],"n":[9],"\u2264":[10],"6":[11],"nodes.":[12],"The":[13],"celebrated":[14],"Graph":[15],"Isomorphism":[16],"Problem":[17],"(GIP)":[18],"consists":[19],"in":[20],"deciding":[21],"whether":[22,31],"or":[23,124],"not":[24],"two":[25,74],"given":[26],"graphs":[27,75],"are":[28,76,117],"isomorphic,":[29],"i.e.,":[30],"there":[32],"is":[33,51,111],"bijective":[35],"mapping":[36],"from":[37],"the":[38,46,62,84,96,120],"nodes":[39],"of":[40,45,69,92,106,126],"onto":[43],"those":[44,115],"other":[47],"such":[48],"that":[49,102,116],"adjacency":[50,122],"preserved.":[52],"An":[53],"interesting":[54],"algorithmic":[55],"approach":[56],"isomorphism":[59],"problem":[60],"uses":[61],"\u201ccode\u201d":[63],"(sometimes":[64],"called":[65],"complete":[67,90,104],"system":[68,105],"invariants).":[70],"Following":[71],"this":[72],"approach,":[73],"isomorphic":[77],"if":[78,81],"and":[79],"only":[80],"they":[82],"have":[83],"same":[85],"code.":[86],"propose":[88],"several":[89],"sets":[91],"invariants":[93,107],"settle":[95],"GIP":[97],"for":[98,108,114],"graphs.":[100],"Note":[101],"no":[103],"known,":[112],"except":[113],"equivalent":[118],"entire":[121],"matrix":[123],"list":[125],"adjacencies.":[127]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
