{"id":"https://openalex.org/W2625224627","doi":"https://doi.org/10.1080/10586458.2017.1391725","title":"On Functional Graphs of Quadratic Polynomials","display_name":"On Functional Graphs of Quadratic Polynomials","publication_year":2017,"publication_date":"2017-11-29","ids":{"openalex":"https://openalex.org/W2625224627","doi":"https://doi.org/10.1080/10586458.2017.1391725","mag":"2625224627"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2017.1391725","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1391725","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"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":"Experimental Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1706.04734","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071932180","display_name":"Bernard Mans","orcid":"https://orcid.org/0000-0001-7897-2043"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Bernard Mans","raw_affiliation_strings":["Department of Computing, Macquarie University, Sydney, NSW, Australia","Department of Computing, Macquarie University, Sydney NSW Australia"],"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Department of Computing, Macquarie University, Sydney NSW Australia","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054948977","display_name":"Min Sha","orcid":"https://orcid.org/0000-0003-2326-559X"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Min Sha","raw_affiliation_strings":["Department of Computing, Macquarie University, Sydney, NSW, Australia","Department of Computing, Macquarie University, Sydney NSW Australia"],"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Department of Computing, Macquarie University, Sydney NSW Australia","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030033231","display_name":"Igor E. Shparlinski","orcid":"https://orcid.org/0000-0002-5246-9391"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Igor E. Shparlinski","raw_affiliation_strings":["Department of Pure Mathematics, University of New South Wales, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of New South Wales, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043415368","display_name":"Daniel Sutantyo","orcid":null},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Daniel Sutantyo","raw_affiliation_strings":["Department of Computing, Macquarie University, Sydney, NSW, Australia","Department of Computing, Macquarie University, Sydney NSW Australia"],"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Department of Computing, Macquarie University, Sydney NSW Australia","institution_ids":["https://openalex.org/I99043593"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5054948977"],"corresponding_institution_ids":["https://openalex.org/I99043593"],"apc_list":null,"apc_paid":null,"fwci":0.4274,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59226858,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"3","first_page":"292","last_page":"300"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9991000294685364,"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":0.9991000294685364,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9828000068664551,"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/mathematics","display_name":"Mathematics","score":0.6077079176902771},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5687376856803894},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5107877254486084},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.49613556265830994},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.49242720007896423},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48730218410491943},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.4871520698070526},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4832349717617035},{"id":"https://openalex.org/keywords/modular-decomposition","display_name":"Modular decomposition","score":0.4667755663394928},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3272501826286316},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2300601601600647},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15728923678398132},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.09841269254684448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6077079176902771},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5687376856803894},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5107877254486084},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.49613556265830994},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.49242720007896423},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48730218410491943},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.4871520698070526},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4832349717617035},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.4667755663394928},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3272501826286316},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2300601601600647},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15728923678398132},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.09841269254684448},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10586458.2017.1391725","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1391725","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"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":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1706.04734","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.04734","pdf_url":"https://arxiv.org/pdf/1706.04734","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2625224627","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1706.04734.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1706.04734","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1706.04734","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1706.04734","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.04734","pdf_url":"https://arxiv.org/pdf/1706.04734","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320591","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2625224627.pdf","grobid_xml":"https://content.openalex.org/works/W2625224627.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W315047097","https://openalex.org/W1513023431","https://openalex.org/W1578973799","https://openalex.org/W1714148690","https://openalex.org/W1967501566","https://openalex.org/W1982618205","https://openalex.org/W1992443722","https://openalex.org/W2031181819","https://openalex.org/W2058177166","https://openalex.org/W2069039276","https://openalex.org/W2104661354","https://openalex.org/W2139563752","https://openalex.org/W2155112291","https://openalex.org/W2168559467","https://openalex.org/W2226303357","https://openalex.org/W2257655051","https://openalex.org/W2527346563","https://openalex.org/W2950419884","https://openalex.org/W2962773686","https://openalex.org/W4402623008"],"related_works":["https://openalex.org/W1971728216","https://openalex.org/W2138204011","https://openalex.org/W2922366535","https://openalex.org/W2951363939","https://openalex.org/W2758407290","https://openalex.org/W2952817960","https://openalex.org/W2042732675","https://openalex.org/W3110915506","https://openalex.org/W3036331198","https://openalex.org/W2949641092","https://openalex.org/W2062123715","https://openalex.org/W2149370230","https://openalex.org/W2950802711","https://openalex.org/W2207927997","https://openalex.org/W2511773204","https://openalex.org/W2783791424","https://openalex.org/W3184371534","https://openalex.org/W2152159410","https://openalex.org/W2974988387","https://openalex.org/W2189101969"],"abstract_inverted_index":{"We":[0,11,72],"study":[1],"functional":[2,37,70,77,111],"graphs":[3,42,82,112],"generated":[4],"by":[5],"quadratic":[6],"polynomials":[7],"over":[8],"prime":[9],"fields.":[10],"introduce":[12],"efficient":[13],"algorithms":[14],"for":[15],"methodical":[16],"computations":[17],"and":[18,25,107,113],"provide":[19],"the":[20,33,39,47,54,64,81,95,105],"values":[21],"of":[22,29,35,41,49,51,56,58,66,97],"various":[23],"direct":[24],"cumulative":[26],"statistical":[27],"parameters":[28],"interest.":[30],"These":[31],"include:":[32],"number":[34,40,48,55],"connected":[36,76],"graphs,":[38,78],"having":[43],"a":[44],"maximal":[45],"cycle,":[46],"cycles":[50],"fixed":[52,59],"size,":[53,60],"components":[57],"as":[61,63],"well":[62],"shape":[65],"trees":[67],"extracted":[68],"from":[69],"graphs.":[71],"particularly":[73],"focus":[74],"on":[75,94],"that":[79,83],"is,":[80],"contain":[84],"only":[85,90],"one":[86,91],"component":[87],"(and":[88],"thus":[89],"cycle).":[92],"Based":[93],"results":[96],"our":[98],"computations,":[99],"we":[100],"formulate":[101],"several":[102],"conjectures":[103],"highlighting":[104],"similarities":[106],"differences":[108],"between":[109],"these":[110],"random":[114],"mappings.":[115]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}