{"id":"https://openalex.org/W4417307734","doi":"https://doi.org/10.2197/ipsjjip.33.1049","title":"Number of Fixed Points of <i>k</i>-Almost and <i>k</i>-Nearly Quadratic Digraphs Associated with <i>x</i><sup>2</sup> \u2261 <i>y</i> \u00b1 <i>k</i>(mod <i>p</i>) where <i>k</i> \u2208 {1,2,3} and <i>p</i> is an Odd Prime","display_name":"Number of Fixed Points of <i>k</i>-Almost and <i>k</i>-Nearly Quadratic Digraphs Associated with <i>x</i><sup>2</sup> \u2261 <i>y</i> \u00b1 <i>k</i>(mod <i>p</i>) where <i>k</i> \u2208 {1,2,3} and <i>p</i> is an Odd Prime","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4417307734","doi":"https://doi.org/10.2197/ipsjjip.33.1049"},"language":"en","primary_location":{"id":"doi:10.2197/ipsjjip.33.1049","is_oa":true,"landing_page_url":"https://doi.org/10.2197/ipsjjip.33.1049","pdf_url":"https://www.jstage.jst.go.jp/article/ipsjjip/33/0/33_1049/_pdf","source":{"id":"https://openalex.org/S4210239267","display_name":"Journal of Information Processing","issn_l":"1882-6652","issn":["1882-6652"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Information Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.jstage.jst.go.jp/article/ipsjjip/33/0/33_1049/_pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054717146","display_name":"Ratinan Boonklurb","orcid":"https://orcid.org/0000-0003-0189-7799"},"institutions":[{"id":"https://openalex.org/I158708052","display_name":"Chulalongkorn University","ror":"https://ror.org/028wp3y58","country_code":"TH","type":"education","lineage":["https://openalex.org/I158708052"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Ratinan Boonklurb","raw_affiliation_strings":["Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University","institution_ids":["https://openalex.org/I158708052"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010846886","display_name":"Pinkaew Siriwong","orcid":null},"institutions":[{"id":"https://openalex.org/I79246082","display_name":"Thaksin University","ror":"https://ror.org/00t2prd39","country_code":"TH","type":"education","lineage":["https://openalex.org/I79246082"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Pinkaew Siriwong","raw_affiliation_strings":["Mathematics and Data Management Program, Faculty of Science and Digital Innovation, Thaksin University"],"affiliations":[{"raw_affiliation_string":"Mathematics and Data Management Program, Faculty of Science and Digital Innovation, Thaksin University","institution_ids":["https://openalex.org/I79246082"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054717146"],"corresponding_institution_ids":["https://openalex.org/I158708052"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3982794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"0","first_page":"1049","last_page":"1055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.5120000243186951,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.5120000243186951,"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/T11130","display_name":"Coding theory and cryptography","score":0.14589999616146088,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.11180000007152557,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/digraph","display_name":"Digraph","score":0.8736000061035156},{"id":"https://openalex.org/keywords/quadratic-residue","display_name":"Quadratic residue","score":0.7746999859809875},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6442000269889832},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6310999989509583},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.45829999446868896},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.45320001244544983},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.35920000076293945},{"id":"https://openalex.org/keywords/prime-number","display_name":"Prime number","score":0.34860000014305115}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.8736000061035156},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7804999947547913},{"id":"https://openalex.org/C12817185","wikidata":"https://www.wikidata.org/wiki/Q878259","display_name":"Quadratic residue","level":2,"score":0.7746999859809875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6550999879837036},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6442000269889832},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6310999989509583},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5146999955177307},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.45829999446868896},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.35920000076293945},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.34860000014305115},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C165656649","wikidata":"https://www.wikidata.org/wiki/Q748339","display_name":"Legendre symbol","level":5,"score":0.30239999294281006},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C95136341","wikidata":"https://www.wikidata.org/wiki/Q625519","display_name":"Quadratic field","level":4,"score":0.27799999713897705},{"id":"https://openalex.org/C152022596","wikidata":"https://www.wikidata.org/wiki/Q7268361","display_name":"Quadratic form (statistics)","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C80695182","wikidata":"https://www.wikidata.org/wiki/Q864134","display_name":"Binary quadratic form","level":4,"score":0.2646999955177307},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.2583000063896179},{"id":"https://openalex.org/C19875773","wikidata":"https://www.wikidata.org/wiki/Q803531","display_name":"Quadratic integer","level":3,"score":0.25589999556541443}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2197/ipsjjip.33.1049","is_oa":true,"landing_page_url":"https://doi.org/10.2197/ipsjjip.33.1049","pdf_url":"https://www.jstage.jst.go.jp/article/ipsjjip/33/0/33_1049/_pdf","source":{"id":"https://openalex.org/S4210239267","display_name":"Journal of Information Processing","issn_l":"1882-6652","issn":["1882-6652"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Information Processing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2197/ipsjjip.33.1049","is_oa":true,"landing_page_url":"https://doi.org/10.2197/ipsjjip.33.1049","pdf_url":"https://www.jstage.jst.go.jp/article/ipsjjip/33/0/33_1049/_pdf","source":{"id":"https://openalex.org/S4210239267","display_name":"Journal of Information Processing","issn_l":"1882-6652","issn":["1882-6652"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Information Processing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321557","display_name":"Chulalongkorn University","ror":"https://ror.org/028wp3y58"},{"id":"https://openalex.org/F4320329431","display_name":"Thaksin University","ror":"https://ror.org/00t2prd39"},{"id":"https://openalex.org/F4320336321","display_name":"Faculty of Science, Chulalongkorn University","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4417307734.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1987023204","https://openalex.org/W2000009242","https://openalex.org/W2002257546","https://openalex.org/W2033571929","https://openalex.org/W2056833032","https://openalex.org/W2247270304","https://openalex.org/W2317594392","https://openalex.org/W2323383120","https://openalex.org/W2469032810","https://openalex.org/W3002113783","https://openalex.org/W3130951907","https://openalex.org/W3207238203","https://openalex.org/W4402919017"],"related_works":[],"abstract_inverted_index":{"Let":[0,97],"n":[1,20],"and":[2,47,136],"k":[3,141],"be":[4,99],"positive":[5],"integers.":[6],"We":[7,103],"define":[8],"a":[9,51,59,63,109],"quadratic":[10,82,95,110,138],"digraph":[11,111,139],"G+(-)(2,":[12,26,55,74,86,112],"k,":[13,27,56,75,113],"n)":[14,28,57,76,88],"over":[15],"the":[16,22,30,79,92,105,117,129],"residue":[17,34],"classes":[18],"of":[19,25,32,36,54,108,131,134],"where":[21,140],"vertex":[23,60,64],"set":[24,31],"is":[29,50,77,89,121],"complete":[33],"class":[35],"all":[37],"integers":[38],"when":[39,119],"divided":[40,122],"by":[41,123],"n,":[42],"{0,":[43],"1,":[44,87],"2,...,":[45],"n-1}":[46],"(u,":[48],"v)":[49],"directed":[52],"edge":[53],"from":[58],"u":[61],"to":[62],"v":[65,69],"if":[66],"u2":[67],"\u2261":[68],"+":[70],"(-)k":[71],"(mod":[72],"n).":[73],"called":[78,91],"k-almost":[80,135],"(k-nearly)":[81],"digraph.":[83,96],"When":[84],"k=1,":[85],"also":[90],"almost":[93],"(nearly)":[94],"p":[98,120],"an":[100],"odd":[101],"prime.":[102],"consider":[104],"fixed":[106,132],"points":[107,133],"p).":[114],"Depending":[115],"on":[116],"remainder":[118],"certain":[124],"prime":[125],"numbers,":[126],"we":[127],"obtain":[128],"number":[130],"k-nearly":[137],"\u2208":[142],"{1,":[143],"2,":[144],"3}.":[145]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-12-14T00:00:00"}