{"id":"https://openalex.org/W1563371187","doi":"https://doi.org/10.37236/3331","title":"Skew Spectra of Oriented Bipartite Graphs","display_name":"Skew Spectra of Oriented Bipartite Graphs","publication_year":2013,"publication_date":"2013-11-15","ids":{"openalex":"https://openalex.org/W1563371187","doi":"https://doi.org/10.37236/3331","mag":"1563371187"},"language":"en","primary_location":{"id":"doi:10.37236/3331","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3331","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i4p18/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/v20i4p18/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029819966","display_name":"A. Anuradha","orcid":"https://orcid.org/0000-0002-2200-688X"},"institutions":[{"id":"https://openalex.org/I4076070","display_name":"Bharathidasan University","ror":"https://ror.org/02w7vnb60","country_code":"IN","type":"education","lineage":["https://openalex.org/I4076070"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"A. Anuradha","raw_affiliation_strings":["Department of Mathematics Bharathidasan University Tiruchirappalli 620024, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Bharathidasan University Tiruchirappalli 620024, India","institution_ids":["https://openalex.org/I4076070"]}]},{"author_position":"middle","author":{"id":null,"display_name":"R. Balakrishnan","orcid":null},"institutions":[{"id":"https://openalex.org/I4076070","display_name":"Bharathidasan University","ror":"https://ror.org/02w7vnb60","country_code":"IN","type":"education","lineage":["https://openalex.org/I4076070"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"R. Balakrishnan","raw_affiliation_strings":["Department of Mathematics Bharathidasan University Tiruchirappalli 620024, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Bharathidasan University Tiruchirappalli 620024, India","institution_ids":["https://openalex.org/I4076070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100693583","display_name":"Xiaolin Chen","orcid":"https://orcid.org/0000-0002-2599-2013"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaolin Chen","raw_affiliation_strings":["Center for Combinatorics and LPMC-TJKLC Nankai University Tianjin 300071, P. R. China"],"affiliations":[{"raw_affiliation_string":"Center for Combinatorics and LPMC-TJKLC Nankai University Tianjin 300071, P. R. China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108139512","display_name":"Xueliang Li","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xueliang Li","raw_affiliation_strings":["Center for Combinatorics and LPMC-TJKLC Nankai University Tianjin 300071, P. R. China"],"affiliations":[{"raw_affiliation_string":"Center for Combinatorics and LPMC-TJKLC Nankai University Tianjin 300071, P. R. China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103169359","display_name":"Huishu Lian","orcid":"https://orcid.org/0000-0003-4208-3927"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huishu Lian","raw_affiliation_strings":["Center for Combinatorics and LPMC-TJKLC Nankai University Tianjin 300071, P. R. China"],"affiliations":[{"raw_affiliation_string":"Center for Combinatorics and LPMC-TJKLC Nankai University Tianjin 300071, P. R. China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070481718","display_name":"Wasin So","orcid":null},"institutions":[{"id":"https://openalex.org/I51504820","display_name":"San Jose State University","ror":"https://ror.org/04qyvz380","country_code":"US","type":"education","lineage":["https://openalex.org/I51504820"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wasin So","raw_affiliation_strings":["Department of Mathematics San Jose State University San Jose, California 95192-0103, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics San Jose State University San Jose, California 95192-0103, U.S.A","institution_ids":["https://openalex.org/I51504820"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5070481718"],"corresponding_institution_ids":["https://openalex.org/I51504820"],"apc_list":null,"apc_paid":null,"fwci":5.3737,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.9543921,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"20","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"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":0.9997000098228455,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8326491117477417},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8197417259216309},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7767072916030884},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.7529584169387817},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5452620387077332},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.531959056854248},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.4633638560771942},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.4479587972164154},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.44377437233924866},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38386279344558716},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10125845670700073},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10043087601661682}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8326491117477417},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8197417259216309},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7767072916030884},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.7529584169387817},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5452620387077332},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.531959056854248},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.4633638560771942},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.4479587972164154},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.44377437233924866},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38386279344558716},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10125845670700073},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10043087601661682},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/3331","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3331","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i4p18/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"}],"best_oa_location":{"id":"doi:10.37236/3331","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3331","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i4p18/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/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3349725324","display_name":null,"funder_award_id":"SR/S4/MS","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G4018744250","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G4412498071","display_name":null,"funder_award_id":"India","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1563371187.pdf","grobid_xml":"https://content.openalex.org/works/W1563371187.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W104699044","https://openalex.org/W1483788020","https://openalex.org/W1493587381","https://openalex.org/W1512332135","https://openalex.org/W1972151784","https://openalex.org/W1998283131","https://openalex.org/W2023145669","https://openalex.org/W2050449391","https://openalex.org/W2063314964","https://openalex.org/W2141383715","https://openalex.org/W2147535338","https://openalex.org/W3000665279","https://openalex.org/W6628789132","https://openalex.org/W6630745428","https://openalex.org/W6649707328","https://openalex.org/W6655974766","https://openalex.org/W6666005358","https://openalex.org/W6681663516","https://openalex.org/W6773054859","https://openalex.org/W6805452137","https://openalex.org/W6811817532"],"related_works":["https://openalex.org/W2916710807","https://openalex.org/W4286907761","https://openalex.org/W2413588304","https://openalex.org/W3205447645","https://openalex.org/W2009411567","https://openalex.org/W2371629703","https://openalex.org/W2097769911","https://openalex.org/W2033835720","https://openalex.org/W3087772622","https://openalex.org/W4322716869"],"abstract_inverted_index":{"A":[0],"graph":[1,156],"$G$":[2,91],"is":[3,18,25,34,119],"said":[4],"to":[5,36,41,121,185],"have":[6],"a":[7,72,135,154,158,174],"parity-linked":[8],"orientation":[9,79,89,124,148],"$\\phi$":[10,86,118],"if":[11,114,117],"every":[12],"even":[13,26],"cycle":[14],"$C_{2k}$":[15],"in":[16],"$G^{\\phi}$":[17,103],"evenly":[19],"(resp.":[20,27],"oddly)":[21],"oriented":[22,139,169,190],"whenever":[23],"$k$":[24],"odd).":[28],"In":[29],"this":[30,32,128,181],"paper,":[31],"concept":[33],"used":[35,184],"provide":[37],"an":[38,147],"affirmative":[39],"answer":[40],"the":[42,56,76,82,99,105,122,132,150,163,167],"following":[43],"conjecture":[44],"of":[45,59,62,80,90,102,107,125,138,149,153,166,176,189],"D.":[46],"Cui":[47,177],"and":[48,92,95,104,115,157,160,178],"Y.":[49,53],"Hou":[50],"[D.":[51],"Cui,":[52],"Hou,":[54],"On":[55],"skew":[57,100,164,194],"spectra":[58],"Cartesian":[60,151],"products":[61],"graphs,":[63],"Electronic":[64],"J.":[65],"Combin.":[66],"20(2):#P19,":[67],"2013]:":[68],"Let":[69,85],"$G=G(X,Y)$":[70],"be":[71,87,183],"bipartite":[73,155],"graph.":[74],"Call":[75],"$X\\rightarrow":[77],"Y$":[78],"$G,$":[81],"canonical":[83,123],"orientation.":[84],"any":[88],"let":[93],"$Sp_S(G^{\\phi})$":[94],"$Sp(G)$":[96],"denote":[97],"respectively":[98],"spectrum":[101,106,165],"$G.$":[108,126],"Then":[109],"$Sp_S(G^{\\phi})":[110],"=":[111],"{\\bf{i}}":[112],"Sp(G)$":[113],"only":[116],"switching-equivalent":[120],"Using":[127],"result,":[129],"we":[130,145],"determine":[131,162],"switch":[133],"for":[134],"special":[136],"family":[137],"hypercubes":[140],"$Q_d^{\\phi},$":[141],"$d\\geq":[142],"1.$":[143],"Moreover,":[144],"give":[146],"product":[152,170],"graph,":[159,171],"then":[161],"resulting":[168],"which":[172],"generalizes":[173],"result":[175],"Hou.":[179],"Further":[180],"can":[182],"construct":[186],"new":[187],"families":[188],"graphs":[191],"with":[192],"maximum":[193],"energy.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}