{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:09:10Z","timestamp":1753888150698,"version":"3.41.2"},"reference-count":27,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T00:00:00Z","timestamp":1635465600000},"content-version":"vor","delay-in-days":301,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100008050","name":"University of Shanghai for Science and Technology","doi-asserted-by":"publisher","award":["10-20-303-302"],"award-info":[{"award-number":["10-20-303-302"]}],"id":[{"id":"10.13039\/501100008050","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Let <jats:italic>G<\/jats:italic> = (<jats:italic>V<\/jats:italic><jats:sub><jats:italic>G<\/jats:italic><\/jats:sub>, <jats:italic>E<\/jats:italic><jats:sub><jats:italic>G<\/jats:italic><\/jats:sub>) be the connected graph. For any vertex <jats:italic>i<\/jats:italic> \u2208 <jats:italic>V<\/jats:italic><jats:sub><jats:italic>G<\/jats:italic><\/jats:sub> and a subset <jats:italic>B<\/jats:italic>\u2286<jats:italic>V<\/jats:italic><jats:sub><jats:italic>G<\/jats:italic><\/jats:sub>, the distance between <jats:italic>i<\/jats:italic> and <jats:italic>B<\/jats:italic> is <jats:italic>d<\/jats:italic>(<jats:italic>i<\/jats:italic>; <jats:italic>B<\/jats:italic>) = min{<jats:italic>d<\/jats:italic>(<jats:italic>i<\/jats:italic>, <jats:italic>j<\/jats:italic>)<jats:italic>|<\/jats:italic><jats:italic>j<\/jats:italic> \u2208 <jats:italic>B<\/jats:italic>}. The ordered <jats:italic>k<\/jats:italic>\u2010partition of <jats:italic>V<\/jats:italic><jats:sub><jats:italic>G<\/jats:italic><\/jats:sub> is \u03a0 = {<jats:italic>B<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>B<\/jats:italic><jats:sub>2<\/jats:sub>, \u2026, <jats:italic>B<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>}. The representation of vertex <jats:italic>i<\/jats:italic> with respect to \u03a0 is the <jats:italic>k<\/jats:italic>\u2010vector, that is, <jats:italic>r<\/jats:italic>(<jats:italic>i<\/jats:italic><jats:italic>|<\/jats:italic>\u03a0) = (<jats:italic>d<\/jats:italic>(<jats:italic>i<\/jats:italic>, <jats:italic>B<\/jats:italic><jats:sub>1<\/jats:sub>), <jats:italic>d<\/jats:italic>(<jats:italic>i<\/jats:italic>, <jats:italic>B<\/jats:italic><jats:sub>2<\/jats:sub>), \u2026, <jats:italic>d<\/jats:italic>(<jats:italic>i<\/jats:italic>, <jats:italic>B<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>)). The partition \u03a0 is called the resolving (distinguishing) partition if <jats:italic>r<\/jats:italic>(<jats:italic>i<\/jats:italic><jats:italic>|<\/jats:italic>\u03a0) \u2260 <jats:italic>r<\/jats:italic>(<jats:italic>j<\/jats:italic><jats:italic>|<\/jats:italic>\u03a0), for all distinct <jats:italic>i<\/jats:italic>, <jats:italic>j<\/jats:italic> \u2208 <jats:italic>V<\/jats:italic><jats:sub><jats:italic>G<\/jats:italic><\/jats:sub>. The minimum cardinality of the resolving partition is called the partition dimension, denoted as pd(<jats:italic>G<\/jats:italic>). In this paper, we consider the upper bound for the partition dimension of the generalized Petersen graph in terms of the cardinalities of its partite sets.<\/jats:p>","DOI":"10.1155\/2021\/5592476","type":"journal-article","created":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T20:05:06Z","timestamp":1635537906000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Partition Dimension of Generalized Petersen Graph"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1477-3608","authenticated-orcid":false,"given":"Hassan","family":"Raza","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9620-7692","authenticated-orcid":false,"given":"Jia-Bao","family":"Liu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5181-4221","authenticated-orcid":false,"given":"Muhammad","family":"Azeem","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3175-7191","authenticated-orcid":false,"given":"Muhammad Faisal","family":"Nadeem","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,10,29]]},"reference":[{"key":"e_1_2_9_1_2","first-page":"549","article-title":"Leaves of trees","volume":"14","author":"Slater P. 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