{"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":true,"raw_author_name":"Frank Harary","raw_affiliation_strings":["\n 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"],"affiliations":[{"raw_affiliation_string":"\n 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":["\n Department of Computer Science, University of Cyprus, CY, Nicosia, 1789, Cyprus","Department of Computer Science , University of Cyprus , CY, Nicosia, 1789, Cyprus"],"affiliations":[{"raw_affiliation_string":"\n 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":["https://openalex.org/A5111801246"],"corresponding_institution_ids":["https://openalex.org/I10052268"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.2259478,"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":{"Abstract":[0],"We":[1,88],"define":[2],"a":[3,35,67,110],"small":[4,100],"graph":[5,43,59,111],"to":[6,58,95,120],"be":[7],"one":[8,42],"with":[9],"n":[10],"\u2264":[11],"6":[12],"nodes.":[13],"The":[14],"celebrated":[15],"Graph":[16,130],"Isomorphism":[17],"Problem":[18],"(GIP)":[19],"consists":[20],"in":[21],"deciding":[22],"whether":[23,32],"or":[24,125],"not":[25],"two":[26,75],"given":[27],"graphs":[28,76],"are":[29,77,118],"isomorphic,":[30],"i.e.,":[31],"there":[33],"is":[34,52,112],"bijective":[36],"mapping":[37],"from":[38],"the":[39,47,63,85,97,121],"nodes":[40],"of":[41,46,70,93,107,127,134],"onto":[44],"those":[45,116],"other":[48],"such":[49],"that":[50,103,117],"adjacency":[51,123],"preserved.":[53],"An":[54],"interesting":[55],"algorithmic":[56],"approach":[57],"isomorphism":[60,131],"problem":[61],"uses":[62],"\u201ccode\u201d":[64],"(sometimes":[65],"called":[66],"complete":[68,91,105],"system":[69,106,133],"invariants).":[71],"Following":[72],"this":[73],"approach,":[74],"isomorphic":[78],"if":[79,82],"and":[80],"only":[81],"they":[83],"have":[84],"same":[86],"code.":[87],"propose":[89],"several":[90],"sets":[92],"invariants":[94,108],"settle":[96],"GIP":[98],"for":[99,109,115],"graphs.":[101],"Note":[102],"no":[104],"known,":[113],"except":[114],"equivalent":[119],"entire":[122],"matrix":[124],"list":[126],"adjacencies.":[128],"Keywords:":[129],"problemcomplete":[132],"invariantsdegree":[135],"sequencecycle":[136],"vectoredge":[137],"vectorC.R.Categories:":[138],"F2.2G.2.2":[139]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}