{"id":"https://openalex.org/W4400513382","doi":"https://doi.org/10.61091/ars159-05","title":"Sharp Bounds for the General Randic Index of \\(R\\)-Graph Products","display_name":"Sharp Bounds for the General Randic Index of \\(R\\)-Graph Products","publication_year":2024,"publication_date":"2024-06-30","ids":{"openalex":"https://openalex.org/W4400513382","doi":"https://doi.org/10.61091/ars159-05"},"language":"en","primary_location":{"id":"doi:10.61091/ars159-05","is_oa":true,"landing_page_url":"http://dx.doi.org/10.61091/ars159-05","pdf_url":"https://combinatorialpress.com/article/ars/sharp-bounds-for-the-general-randic-index-of-r-graph-products.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://combinatorialpress.com/article/ars/sharp-bounds-for-the-general-randic-index-of-r-graph-products.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109452577","display_name":"Xiujun Zhang","orcid":"https://orcid.org/0000-0002-6704-031X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiujun Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032946035","display_name":"M.A. Rashid","orcid":"https://orcid.org/0000-0002-9300-4574"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muhammad Aamer Rashid","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20545073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"159","issue":"1","first_page":"41","last_page":"50"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9994000196456909,"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/T10849","display_name":"Finite Group Theory Research","score":0.9994000196456909,"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/T11476","display_name":"Graph theory and applications","score":0.9986000061035156,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9955999851226807,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8677680492401123},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5731385946273804},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.507529616355896},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.4652792811393738},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32319173216819763},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08403566479682922}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8677680492401123},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5731385946273804},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.507529616355896},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.4652792811393738},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32319173216819763},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08403566479682922},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.61091/ars159-05","is_oa":true,"landing_page_url":"http://dx.doi.org/10.61091/ars159-05","pdf_url":"https://combinatorialpress.com/article/ars/sharp-bounds-for-the-general-randic-index-of-r-graph-products.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.61091/ars159-05","is_oa":true,"landing_page_url":"http://dx.doi.org/10.61091/ars159-05","pdf_url":"https://combinatorialpress.com/article/ars/sharp-bounds-for-the-general-randic-index-of-r-graph-products.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3409638970","display_name":null,"funder_award_id":"G00002233","funder_id":"https://openalex.org/F4320323593","funder_display_name":"United Arab Emirates University"},{"id":"https://openalex.org/G5721014023","display_name":null,"funder_award_id":"G00002590","funder_id":"https://openalex.org/F4320323593","funder_display_name":"United Arab Emirates University"}],"funders":[{"id":"https://openalex.org/F4320323593","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400513382.pdf","grobid_xml":"https://content.openalex.org/works/W4400513382.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"A":[0],"chemical":[1],"structure":[2],"specifies":[3],"the":[4,14,53,73],"molecular":[5],"geometry":[6],"of":[7,16,33,58,61,77,84],"a":[8,31,78],"given":[9],"molecule":[10],"or":[11,35],"solid":[12],"in":[13],"form":[15],"atom":[17],"arrangements.":[18],"One":[19],"way":[20],"to":[21,26,46],"analyze":[22],"its":[23,28],"properties":[24],"is":[25],"simulate":[27],"formation":[29],"as":[30],"product":[32,83],"two":[34],"more":[36],"simpler":[37],"graphs.":[38,85],"In":[39],"this":[40,44,69],"article,":[41],"we":[42],"take":[43],"idea":[45],"find":[47],"upper":[48],"and":[49,81],"lower":[50],"bounds":[51,74],"for":[52,75],"generalized":[54],"Randi\u0107":[55],"index":[56],"\\(\\mathcal{R}_{\\alpha}\\)":[57,76],"four":[59],"types":[60],"graph":[62,80],"products,":[63],"using":[64],"combinatorial":[65],"inequalities.":[66],"We":[67],"finish":[68],"paper":[70],"by":[71],"providing":[72],"line":[79],"rooted":[82]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}