{"id":"https://openalex.org/W4213368259","doi":"https://doi.org/10.1142/s1793830922500719","title":"The generalized path matrix and energy","display_name":"The generalized path matrix and energy","publication_year":2022,"publication_date":"2022-02-14","ids":{"openalex":"https://openalex.org/W4213368259","doi":"https://doi.org/10.1142/s1793830922500719"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830922500719","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922500719","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085740580","display_name":"Pengli Lu","orcid":"https://orcid.org/0000-0002-0754-1358"},"institutions":[{"id":"https://openalex.org/I22716506","display_name":"Lanzhou University of Technology","ror":"https://ror.org/03panb555","country_code":"CN","type":"education","lineage":["https://openalex.org/I22716506"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Pengli Lu","raw_affiliation_strings":["School of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, Gansu, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-0754-1358","affiliations":[{"raw_affiliation_string":"School of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, Gansu, P. R. China","institution_ids":["https://openalex.org/I22716506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042822458","display_name":"Rui Luan","orcid":"https://orcid.org/0009-0000-6126-8869"},"institutions":[{"id":"https://openalex.org/I22716506","display_name":"Lanzhou University of Technology","ror":"https://ror.org/03panb555","country_code":"CN","type":"education","lineage":["https://openalex.org/I22716506"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Luan","raw_affiliation_strings":["School of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, Gansu, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, Gansu, P. R. China","institution_ids":["https://openalex.org/I22716506"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085740580"],"corresponding_institution_ids":["https://openalex.org/I22716506"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08574039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"02","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":0.9948999881744385,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9771000146865845,"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/laplacian-matrix","display_name":"Laplacian matrix","score":0.6009716987609863},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5940150022506714},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5912966728210449},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5806636810302734},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.556252658367157},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.47389286756515503},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4457387626171112},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3316843807697296},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19840794801712036},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13122320175170898},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07274821400642395}],"concepts":[{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.6009716987609863},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5940150022506714},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5912966728210449},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5806636810302734},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.556252658367157},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.47389286756515503},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4457387626171112},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3316843807697296},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19840794801712036},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13122320175170898},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07274821400642395},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830922500719","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922500719","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.7799999713897705,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G2819160658","display_name":null,"funder_award_id":"11861045","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3453804540","display_name":null,"funder_award_id":"11361033","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6529624702","display_name":null,"funder_award_id":"62162040","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1966451592","https://openalex.org/W1980222794","https://openalex.org/W1993483106","https://openalex.org/W1996320926","https://openalex.org/W2002653466","https://openalex.org/W2018756269","https://openalex.org/W2024625639","https://openalex.org/W2031324894","https://openalex.org/W2048396151","https://openalex.org/W2066555486","https://openalex.org/W2131467982","https://openalex.org/W2153988305","https://openalex.org/W2167844587","https://openalex.org/W2790264134","https://openalex.org/W2897929224","https://openalex.org/W4210251051","https://openalex.org/W4213151958","https://openalex.org/W4240587491","https://openalex.org/W4295679830"],"related_works":["https://openalex.org/W2165749285","https://openalex.org/W2474979212","https://openalex.org/W2562455930","https://openalex.org/W2001036795","https://openalex.org/W2154748900","https://openalex.org/W3093811938","https://openalex.org/W4390092784","https://openalex.org/W127450631","https://openalex.org/W2062626603","https://openalex.org/W58770712"],"abstract_inverted_index":{"We":[0,92],"define":[1],"the":[2,7,32,40,44,64,86,110],"path":[3,8,33,49,72,87,98,112],"Laplacian":[4,10],"matrix":[5,11,34,42,50,99],"and":[6,22,35,59,106],"signless":[9],"of":[12,43,66,90,96,109,114],"a":[13],"simple":[14],"connected":[15],"graph":[16],"G":[17],"as":[18,77],"[Formula:":[19,23,28,36,52,56,60,67,78,82,100],"see":[20,24,29,37,53,57,61,68,79,83,101],"text]":[21,30,38,58,62,84],"text],":[25,54,80],"respectively,":[26],"where":[27,81],"is":[31,39,51,85],"diagonal":[41],"vertex":[45],"transmissions.":[46],"The":[47,70],"generalized":[48,71,97,111],"for":[55],"are":[63,117],"eigenvalues":[65],"text].":[69,102],"energy":[73,113],"can":[74],"be":[75],"expressed":[76],"Wiener":[88],"index":[89],"G.":[91],"give":[93],"basic":[94],"properties":[95],"Also,":[103],"some":[104,115],"upper":[105],"lower":[107],"bounds":[108],"graphs":[116],"studied.":[118]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
