{"id":"https://openalex.org/W2033014626","doi":"https://doi.org/10.1155/2013/707954","title":"The Distance Matrices of Some Graphs Related to Wheel Graphs","display_name":"The Distance Matrices of Some Graphs Related to Wheel Graphs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2033014626","doi":"https://doi.org/10.1155/2013/707954","mag":"2033014626"},"language":"lv","primary_location":{"id":"doi:10.1155/2013/707954","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/707954","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/707954.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/707954.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101501151","display_name":"Xiao Zhang","orcid":"https://orcid.org/0000-0002-8814-9699"},"institutions":[{"id":"https://openalex.org/I18452120","display_name":"Yantai University","ror":"https://ror.org/01rp41m56","country_code":"CN","type":"education","lineage":["https://openalex.org/I18452120"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoling Zhang","raw_affiliation_strings":["School of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, China","institution_ids":["https://openalex.org/I18452120"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101944250","display_name":"Chengyuan Song","orcid":"https://orcid.org/0000-0002-7493-3546"},"institutions":[{"id":"https://openalex.org/I18452120","display_name":"Yantai University","ror":"https://ror.org/01rp41m56","country_code":"CN","type":"education","lineage":["https://openalex.org/I18452120"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chengyuan Song","raw_affiliation_strings":["School of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, China","institution_ids":["https://openalex.org/I18452120"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101501151"],"corresponding_institution_ids":["https://openalex.org/I18452120"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.3439,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.7917343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9987999796867371,"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":0.9824000000953674,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5252389907836914},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3365384340286255},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29570478200912476}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5252389907836914},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3365384340286255},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29570478200912476}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/707954","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/707954","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/707954.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808026","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808026","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"pmh:oai:RePEc:hin:jnljam:707954","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/707954.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:2186bfe5d5fc4ae480c10c062e04a3f9","is_oa":true,"landing_page_url":"https://doaj.org/article/2186bfe5d5fc4ae480c10c062e04a3f9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/707954","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/707954","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/707954.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1385031454","display_name":null,"funder_award_id":"ZR2012AQ022","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2018752113","display_name":null,"funder_award_id":"11126256","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"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/W2033014626.pdf","grobid_xml":"https://content.openalex.org/works/W2033014626.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1559146381","https://openalex.org/W1964823180","https://openalex.org/W1997175234","https://openalex.org/W2008464768","https://openalex.org/W2022234860","https://openalex.org/W2075048357","https://openalex.org/W2097884181","https://openalex.org/W2111147768","https://openalex.org/W2116451290","https://openalex.org/W2136122855","https://openalex.org/W2785506964","https://openalex.org/W2983896310","https://openalex.org/W4243586797"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Let<mml:math":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1,10,15,22,33,37,43,56],"id=\"M1\"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math>denote":[2],"the":[3,17,47,65],"distance":[4,68,84],"matrix":[5],"of":[6,19,49,67,70],"a":[7,79],"connected":[8],"graph<mml:math":[9],"id=\"M2\"><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>.":[11],"The":[12],"inertia":[13,66],"of<mml:math":[14,55],"id=\"M3\"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math>is":[16],"triple":[18],"integers":[20],"(<mml:math":[21],"id=\"M4\"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msub><mml:mo":[23],"stretchy=\"false\">(</mml:mo><mml:mi>D</mml:mi><mml:mo":[24,27,30,35,40,45],"stretchy=\"false\">)</mml:mo><mml:mo>,</mml:mo><mml:mi>":[25,28],"</mml:mi><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo":[26],"</mml:mi><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo></mml:mrow></mml:msub><mml:mo":[29],"stretchy=\"false\">)</mml:mo></mml:math>),":[31],"where<mml:math":[32],"id=\"M5\"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msub><mml:mo":[34],"stretchy=\"false\">)</mml:mo></mml:math>,<mml:math":[36],"id=\"M6\"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn":[38],"mathvariant=\"normal\">0</mml:mn></mml:mrow></mml:msub><mml:mo":[39],"stretchy=\"false\">)</mml:mo></mml:math>,":[41],"and<mml:math":[42],"id=\"M7\"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo></mml:mrow></mml:msub><mml:mo":[44],"stretchy=\"false\">)</mml:mo></mml:math>denote":[46],"number":[48],"positive,":[50],"0,":[51],"and":[52,77],"negative":[53],"eigenvalues":[54],"id=\"M8\"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math>,":[57],"respectively.":[58],"In":[59],"this":[60],"paper,":[61],"we":[62],"mainly":[63],"study":[64],"matrices":[69,85],"some":[71],"graphs":[72,76,82],"related":[73],"to":[74],"wheel":[75],"give":[78],"construction":[80],"for":[81],"whose":[83],"have":[86],"exactly":[87],"one":[88],"positive":[89],"eigenvalue.":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
