{"id":"https://openalex.org/W2962761224","doi":"https://doi.org/10.11575/cdm.v8i2.62187","title":"The exact maximal energy of integral circulant graphs with prime power order","display_name":"The exact maximal energy of integral circulant graphs with prime power order","publication_year":2012,"publication_date":"2012-11-19","ids":{"openalex":"https://openalex.org/W2962761224","doi":"https://doi.org/10.11575/cdm.v8i2.62187","mag":"2962761224"},"language":"en","primary_location":{"id":"doi:10.11575/cdm.v8i2.62187","is_oa":true,"landing_page_url":"https://doi.org/10.11575/cdm.v8i2.62187","pdf_url":null,"source":{"id":"https://openalex.org/S7407053067","display_name":"University of Calgary","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.11575/cdm.v8i2.62187","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110161267","display_name":"Juergen Sander","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sander, Juergen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054381053","display_name":"Torsten Sander","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sander, Torsten","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110161267"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4323,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.67369379,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":"2","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":1.0,"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":1.0,"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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.8760174512863159},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8455727100372314},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7979228496551514},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6244955062866211},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5667827725410461},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5459474921226501},{"id":"https://openalex.org/keywords/circulant-graph","display_name":"Circulant graph","score":0.5098361372947693},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.49365052580833435},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4913612902164459},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.47912001609802246},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4767143130302429},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.38355380296707153},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.132746160030365},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.07848232984542847},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07304427027702332}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.8760174512863159},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8455727100372314},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7979228496551514},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6244955062866211},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5667827725410461},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5459474921226501},{"id":"https://openalex.org/C82190004","wikidata":"https://www.wikidata.org/wiki/Q5121633","display_name":"Circulant graph","level":5,"score":0.5098361372947693},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.49365052580833435},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4913612902164459},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.47912001609802246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4767143130302429},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38355380296707153},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.132746160030365},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.07848232984542847},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07304427027702332},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.11575/cdm.v8i2.62187","is_oa":true,"landing_page_url":"https://doi.org/10.11575/cdm.v8i2.62187","pdf_url":null,"source":{"id":"https://openalex.org/S7407053067","display_name":"University of Calgary","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:2962761224","is_oa":true,"landing_page_url":"https://cdm.ucalgary.ca/article/download/62187/46759","pdf_url":null,"source":{"id":"https://openalex.org/S2498033248","display_name":"Contributions to Discrete Mathematics","issn_l":"1715-0868","issn":["1715-0868"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310312896","host_organization_name":"University of Calgary Press","host_organization_lineage":["https://openalex.org/P4310312896"],"host_organization_lineage_names":["University of Calgary Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Contributions to Discrete Mathematics","raw_type":null}],"best_oa_location":{"id":"doi:10.11575/cdm.v8i2.62187","is_oa":true,"landing_page_url":"https://doi.org/10.11575/cdm.v8i2.62187","pdf_url":null,"source":{"id":"https://openalex.org/S7407053067","display_name":"University of Calgary","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8700000047683716,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1770246953","https://openalex.org/W1927695923","https://openalex.org/W1994135930","https://openalex.org/W1996992204","https://openalex.org/W2019205401","https://openalex.org/W2060544455","https://openalex.org/W2081655555","https://openalex.org/W2099526591","https://openalex.org/W2149397526","https://openalex.org/W2964138304"],"related_works":["https://openalex.org/W2141892485","https://openalex.org/W2009876987","https://openalex.org/W1996992204","https://openalex.org/W2072535622","https://openalex.org/W2950502676","https://openalex.org/W2375273837","https://openalex.org/W2006138875","https://openalex.org/W2349857754","https://openalex.org/W2951636907","https://openalex.org/W2030613261","https://openalex.org/W2889739240","https://openalex.org/W3142443845","https://openalex.org/W25854198","https://openalex.org/W2084311741","https://openalex.org/W2974582221","https://openalex.org/W3163567768","https://openalex.org/W98581392","https://openalex.org/W2277685783","https://openalex.org/W2962879981","https://openalex.org/W2964300923"],"abstract_inverted_index":{"The":[0],"energy":[1,29,87,103],"of":[2,15,19,22,30,52,54,88,93,110],"a":[3,48,58],"graph":[4,92],"was":[5],"introduced":[6],"by":[7,42],"{\\sc":[8],"Gutman}":[9],"in":[10,56],"1978":[11],"as":[12],"the":[13,16,20,28,86,101],"sum":[14],"absolute":[17],"values":[18],"eigenvalues":[21],"its":[23],"adjacency":[24],"matrix.":[25],"We":[26],"study":[27],"integral":[31,90,107],"circulant":[32,91,108],"graphs,":[33,37],"also":[34],"called":[35],"gcd":[36],"which":[38],"can":[39],"be":[40],"characterized":[41],"their":[43],"vertex":[44,63],"count":[45],"$n$":[46,55],"and":[47,66],"set":[49,64,68],"$\\cal":[50],"D$":[51],"divisors":[53],"such":[57],"way":[59],"that":[60],"they":[61],"have":[62],"$\\mathbb{Z}/n\\mathbb{Z}$":[65],"edge":[67],"$\\{\\{a,b\\}:\\,":[69],"a,b\\in\\mathbb{Z}/n\\mathbb{Z},\\,":[70],"\\gcd(a-b,n)\\in":[71],"{\\cal":[72],"D}\\}$.":[73],"Given":[74],"an":[75,89],"arbitrary":[76],"prime":[77],"power":[78],"$p^s$,":[79],"we":[80],"determine":[81],"all":[82,106],"divisor":[83],"sets":[84],"maximising":[85],"order":[94,111],"$p^s$.":[95,112],"This":[96],"enables":[97],"us":[98],"to":[99],"compute":[100],"maximal":[102],"$\\Emax{p^s}$":[104],"among":[105],"graphs":[109]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
