{"id":"https://openalex.org/W7126041902","doi":"https://doi.org/10.30598/barekengvol20iss2pp1155-1166","title":"THE METRIC DIMENSION OF CYCLE BOOK GRAPHS B_(C_(m,n) ) FORMED BY A COMMON PATH P_2","display_name":"THE METRIC DIMENSION OF CYCLE BOOK GRAPHS B_(C_(m,n) ) FORMED BY A COMMON PATH P_2","publication_year":2026,"publication_date":"2026-01-26","ids":{"openalex":"https://openalex.org/W7126041902","doi":"https://doi.org/10.30598/barekengvol20iss2pp1155-1166"},"language":"en","primary_location":{"id":"doi:10.30598/barekengvol20iss2pp1155-1166","doi":"https://doi.org/10.30598/barekengvol20iss2pp1155-1166","is_oa":true,"landing_page_url":"https://doi.org/10.30598/barekengvol20iss2pp1155-1166","pdf_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/18844/12447","source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/18844/12447","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035058410","display_name":"Jaya Santoso","orcid":"https://orcid.org/0009-0001-7329-3137","observed_orcids":["https://orcid.org/0009-0001-7329-3137"]},"institutions":[{"id":"https://openalex.org/I4405263114","display_name":"Institut Teknologi Del","ror":"https://ror.org/02r7z4c46","country_code":"ID","type":"education","lineage":["https://openalex.org/I4405263114"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Jaya Santoso","raw_affiliation_strings":["Department of Informatics, Faculty of Informatics and Electrical Engineering, Institut Teknologi Del, Indonesia"],"raw_orcid":"https://orcid.org/0009-0001-7329-3137","affiliations":[{"raw_affiliation_string":"Department of Informatics, Faculty of Informatics and Electrical Engineering, Institut Teknologi Del, Indonesia","institution_ids":["https://openalex.org/I4405263114"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159803634","display_name":"Darmaji Darmaji","orcid":"https://orcid.org/0009-0000-5213-1334","observed_orcids":["https://orcid.org/0009-0000-5213-1334"]},"institutions":[{"id":"https://openalex.org/I166843116","display_name":"Institut Teknologi Sepuluh Nopember","ror":"https://ror.org/05kbmmt89","country_code":"ID","type":"education","lineage":["https://openalex.org/I166843116"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Darmaji Darmaji","raw_affiliation_strings":["2Department of Mathematics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember Gedung G Lantai 2, Indonesia"],"raw_orcid":"https://orcid.org/0009-0000-5213-1334","affiliations":[{"raw_affiliation_string":"2Department of Mathematics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember Gedung G Lantai 2, Indonesia","institution_ids":["https://openalex.org/I166843116"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077188691","display_name":"Ana Muliyana","orcid":"https://orcid.org/0009-0004-6304-0058","observed_orcids":["https://orcid.org/0009-0004-6304-0058"]},"institutions":[{"id":"https://openalex.org/I4405263114","display_name":"Institut Teknologi Del","ror":"https://ror.org/02r7z4c46","country_code":"ID","type":"education","lineage":["https://openalex.org/I4405263114"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Ana Muliyana","raw_affiliation_strings":["Software Engineering Technology, Faculty of Vocational, Institut Teknologi Del, Indonesia"],"raw_orcid":"https://orcid.org/0009-0004-6304-0058","affiliations":[{"raw_affiliation_string":"Software Engineering Technology, Faculty of Vocational, Institut Teknologi Del, Indonesia","institution_ids":["https://openalex.org/I4405263114"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084987645","display_name":"Asido Saragih","orcid":"https://orcid.org/0009-0007-8851-3490","observed_orcids":["https://orcid.org/0009-0007-8851-3490"]},"institutions":[{"id":"https://openalex.org/I4405263114","display_name":"Institut Teknologi Del","ror":"https://ror.org/02r7z4c46","country_code":"ID","type":"education","lineage":["https://openalex.org/I4405263114"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Asido Saragih","raw_affiliation_strings":["Department of Electrical Engineering, Faculty of Informatics and Electrical Engineering, Institut Teknologi Del, Indonesia"],"raw_orcid":"https://orcid.org/0009-0007-8851-3490","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Faculty of Informatics and Electrical Engineering, Institut Teknologi Del, Indonesia","institution_ids":["https://openalex.org/I4405263114"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4926,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.84027205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"20","issue":"2","first_page":"1155","last_page":"1166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9810000061988831,"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"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9810000061988831,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.008500000461935997,"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/T11476","display_name":"Graph theory and applications","score":0.006200000178068876,"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/metric-dimension","display_name":"metric dimension","score":0.9959999918937683},{"id":"https://openalex.org/keywords/cyclic-graphs","display_name":"cyclic graphs","score":0.3700000047683716}],"concepts":[{"id":"https://openalex.org/C60933471","wikidata":"https://www.wikidata.org/wiki/Q17152964","display_name":"Metric dimension","level":5,"score":0.8341000080108643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7106999754905701},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6348000168800354},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5669000148773193},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.531499981880188},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49540001153945923},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.45080000162124634},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C80661125","wikidata":"https://www.wikidata.org/wiki/Q5404299","display_name":"Packing dimension","level":5,"score":0.3458000123500824},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.3077999949455261},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.29260000586509705},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C115311070","wikidata":"https://www.wikidata.org/wiki/Q5347255","display_name":"Effective dimension","level":3,"score":0.27320000529289246},{"id":"https://openalex.org/C54385418","wikidata":"https://www.wikidata.org/wiki/Q2742711","display_name":"Distance","level":4,"score":0.26100000739097595},{"id":"https://openalex.org/C28235433","wikidata":"https://www.wikidata.org/wiki/Q5277259","display_name":"Dimension function","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.30598/barekengvol20iss2pp1155-1166","doi":"https://doi.org/10.30598/barekengvol20iss2pp1155-1166","is_oa":true,"landing_page_url":"https://doi.org/10.30598/barekengvol20iss2pp1155-1166","pdf_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/18844/12447","source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.30598/barekengvol20iss2pp1155-1166","doi":"https://doi.org/10.30598/barekengvol20iss2pp1155-1166","is_oa":true,"landing_page_url":"https://doi.org/10.30598/barekengvol20iss2pp1155-1166","pdf_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/18844/12447","source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7126041902.pdf","grobid_xml":"https://content.openalex.org/works/W7126041902.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1591155714","https://openalex.org/W1886309127","https://openalex.org/W1964684444","https://openalex.org/W2036691208","https://openalex.org/W2037298352","https://openalex.org/W2276402578","https://openalex.org/W2529620030","https://openalex.org/W2791757433","https://openalex.org/W2903382408","https://openalex.org/W2963088986","https://openalex.org/W3012843076","https://openalex.org/W3093837146","https://openalex.org/W3094398669","https://openalex.org/W3131586115","https://openalex.org/W3194637356","https://openalex.org/W3210628496","https://openalex.org/W3212221569","https://openalex.org/W4220893761","https://openalex.org/W4283079617","https://openalex.org/W4313827549","https://openalex.org/W4323768079","https://openalex.org/W4377194538","https://openalex.org/W4391579141","https://openalex.org/W4396828364","https://openalex.org/W4399031039","https://openalex.org/W4400605483","https://openalex.org/W4409055872","https://openalex.org/W4411464034"],"related_works":["https://openalex.org/W4409055872","https://openalex.org/W2791757433","https://openalex.org/W1498734728","https://openalex.org/W3093837146","https://openalex.org/W7111152365","https://openalex.org/W4319753773","https://openalex.org/W3217491740","https://openalex.org/W2895230703","https://openalex.org/W3094398669","https://openalex.org/W3147345490"],"abstract_inverted_index":{"This":[0],"paper":[1,141,281],"investigates":[2,142,282],"the":[3,30,42,68,98,123,143,170,182,208,238,263,283,310,322,348,378,403],"metric":[4,69,99,129,144,209,239,269,284,349,379,409],"dimension":[5,70,100,145,210,240,285,350,380],"of":[6,9,33,74,126,146,149,173,214,266,286,289,313,354,406],"a":[7,19,63,93,147,159,203,233,287,299,343,373],"class":[8,148,288],"graphs":[10,150,290],"known":[11,151,291],"as":[12,152,292],"cycle":[13,75,153,215,293,355],"books,":[14,154,294],"denoted":[15,155,295],"\u200b,":[16,156,296],"which":[17,157,297],"feature":[18,158,298],"shared":[20,160,300],"path":[21,161,301],"\u200b":[22,162,302],"across":[23,163,303],"multiple":[24,164,304],"cycles.":[25,165,305],"We":[26,166,306],"focus":[27,167,307],"on":[28,128,168,268,308,408],"characterizing":[29,169,309],"minimum":[31,171,311],"number":[32,172,312],"vertex":[34,40,174,180,314,320],"subsets":[35,175,315],"required":[36,176,316],"so":[37,177,317],"that":[38,66,81,178,206,221,318,346,361],"each":[39,179,319],"in":[41,131,135,181,271,275,321,411,415],"graph":[43,132,139,183,272,279,323,412,419],"can":[44,184,324],"be":[45,185,325],"uniquely":[46,186,326],"identified":[47,187,327],"by":[48,188,328],"its":[49,189,329],"distances":[50,190,330],"to":[51,122,191,262,331,402],"those":[52,192,332],"subsets.":[53,193,333],"To":[54,194,334],"support":[55,195,335],"our":[56,196,336],"analysis,":[57,197,337],"we":[58,79,91,198,219,231,338,359,371],"present":[59,199,339],"two":[60,200,340],"propositions":[61,201,341],"and":[62,84,105,111,113,117,137,202,224,245,251,253,257,277,342,364,385,391,393,397,417],"general":[64,94,204,234,344,374],"theorem":[65,205,345],"establish":[67,207,347],"for":[71,82,85,88,96,211,222,225,228,236,351,362,365,368,376],"various":[72,212,352],"configurations":[73,213,353],"book":[76,216,356],"graphs.":[77,217,357],"Specifically,":[78,218,358],"prove":[80,220,360],",":[83,86,106,223,226,246,363,366,386],"while":[87,227,367],".":[89,118,229,258,369,398],"Furthermore,":[90,230,370],"provide":[92,232,372],"result":[95,235,375],":":[97,237,377],"is":[101,103,109,115,241,243,249,255,381,383,389,395],"when":[102,108,114,242,248,254,382,388,394],"odd":[104,116,244,256,384,396],"or":[107,247,387],"even":[110,250,390],";":[112,252,392],"These":[119,259,399],"findings":[120,260,400],"contribute":[121,261,401],"growing":[124,264,404],"body":[125,265,405],"knowledge":[127,267,407],"properties":[130,270,410],"theory,":[133,273,413],"particularly":[134,274,414],"structured":[136,276,416],"cyclic":[138,278,418],"families.This":[140,280],"families.":[420]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-01-30T00:00:00"}
