{"id":"https://openalex.org/W7213297403","doi":"https://doi.org/10.48550/arxiv.2609.15133","title":"A proof of the resistance diameter conjecture for line graphs","display_name":"A proof of the resistance diameter conjecture for line graphs","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213297403","doi":"https://doi.org/10.48550/arxiv.2609.15133"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15133","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15133","pdf_url":"https://arxiv.org/pdf/2609.15133","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.15133","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051302370","display_name":"Xiang-Feng Pan","orcid":"https://orcid.org/0000-0001-5301-8739","observed_orcids":["https://orcid.org/0000-0001-5301-8739"]},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pan, Xiang-Feng","raw_affiliation_strings":["School of Mathematical Sciences , Anhui University , Hefei 230601 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Anhui University , Hefei 230601 , China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151875256","display_name":"Xiang-Yang Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Xiang-Yang","raw_affiliation_strings":["School of Mathematical Sciences , Anhui University , Hefei 230601 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Anhui University , Hefei 230601 , China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016940753","display_name":"Zhen\u2010Mu Hong","orcid":"https://orcid.org/0000-0003-1248-0227","observed_orcids":["https://orcid.org/0000-0003-1248-0227"]},"institutions":[{"id":"https://openalex.org/I188935350","display_name":"Anhui University of Finance and Economics","ror":"https://ror.org/0152zzg30","country_code":"CN","type":"education","lineage":["https://openalex.org/I188935350"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong, Zhen-Mu","raw_affiliation_strings":["School of Statistics and Applied Mathematics , Anhui University of Finance & Economics , Bengbu 233030 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics and Applied Mathematics , Anhui University of Finance & Economics , Bengbu 233030 , China","institution_ids":["https://openalex.org/I188935350"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9970999956130981,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.000699999975040555,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0005000000237487257,"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/line-graphs","display_name":"line graphs","score":0.9729999899864197},{"id":"https://openalex.org/keywords/resistance-distance","display_name":"resistance distance","score":0.7480000257492065},{"id":"https://openalex.org/keywords/graph-diameter","display_name":"graph diameter","score":0.5379999876022339},{"id":"https://openalex.org/keywords/electrical-networks","display_name":"electrical networks","score":0.578000009059906},{"id":"https://openalex.org/keywords/cycles","display_name":"cycles","score":0.4350000023841858},{"id":"https://openalex.org/keywords/complete-graph-k4","display_name":"complete graph K4","score":0.9049999713897705}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8317000269889832},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7818999886512756},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6689000129699707},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48820000886917114},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43869999051094055},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.43059998750686646},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.41040000319480896},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.3046000003814697},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.28290000557899475}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.15133","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15133","pdf_url":"https://arxiv.org/pdf/2609.15133","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.15133","doi":"https://doi.org/10.48550/arxiv.2609.15133","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15133","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.15133","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15133","pdf_url":"https://arxiv.org/pdf/2609.15133","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1840432169","display_name":null,"funder_award_id":"12371338","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5180118648","display_name":null,"funder_award_id":"2025AHGXZK30908","funder_id":"https://openalex.org/F4320335406","funder_display_name":"University Natural Science Research Project of Anhui Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326664","display_name":"Anhui Provincial Department of Education","ror":null},{"id":"https://openalex.org/F4320335406","display_name":"University Natural Science Research Project of Anhui Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213297403.pdf","grobid_xml":"https://content.openalex.org/works/W7213297403.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3208070677","https://openalex.org/W2263078115","https://openalex.org/W2264660915","https://openalex.org/W4399455095","https://openalex.org/W4409671303","https://openalex.org/W4376627787","https://openalex.org/W2358058334","https://openalex.org/W2901220709","https://openalex.org/W4223516954","https://openalex.org/W2892127202"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,11,18,66,72,78,88,92],"conjecture":[3],"of":[4,56,80],"Xu,":[5],"Li,":[6],"Hua,":[7],"and":[8,40,83,91],"Pan":[9],"that":[10],"resistance":[12],"diameter":[13,89],"does":[14],"not":[15],"increase":[16],"under":[17],"line-graph":[19],"operation.":[20],"For":[21],"every":[22],"finite":[23],"connected":[24],"simple":[25],"graph":[26],"$G$":[27,43],"with":[28,37,60],"at":[29],"least":[30],"one":[31],"edge,":[32],"we":[33],"establish":[34],"$D_r(L(G))\\le":[35],"D_r(G)$,":[36],"equality":[38,93],"if":[39,42],"only":[41],"is":[44,84],"a":[45,61],"cycle":[46],"or":[47],"$K_4$.":[48],"The":[49],"proof":[50],"combines":[51],"an":[52],"exact":[53],"electrical":[54],"representation":[55],"$L(G)$":[57],"by":[58],"stars":[59],"sharp":[62],"budget":[63],"inequality":[64,70],"for":[65],"branch":[67],"core.":[68],"This":[69],"controls":[71],"combined":[73],"error":[74],"terms":[75],"arising":[76],"from":[77],"comparison":[79],"degree-two":[81],"paths":[82],"central":[85],"to":[86],"both":[87],"bound":[90],"analysis.":[94]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-16T00:00:00"}
