{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:10:40Z","timestamp":1753884640635,"version":"3.41.2"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"Tianjin Normal University Research Innovation Project for Postgraduate Students, China","award":["2023KYCX052Z"],"award-info":[{"award-number":["2023KYCX052Z"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p> A vertex subset [Formula: see text] of a graph [Formula: see text] is a [Formula: see text]-path vertex cover if [Formula: see text] intersects any [Formula: see text]-path in [Formula: see text] for some positive integer [Formula: see text] The minimum magnitude of all [Formula: see text]-path vertex covers is called [Formula: see text]-path vertex cover number of [Formula: see text] (denoted [Formula: see text]). In this contribution, we gave estimations of [Formula: see text] [Formula: see text] and the exact values of [Formula: see text] [Formula: see text] and [Formula: see text]. We also obtain the [Formula: see text] when [Formula: see text] is the Cartesian product of complete and complete bipartite graph. <\/jats:p>","DOI":"10.1142\/s0219265924500221","type":"journal-article","created":{"date-parts":[[2024,11,23]],"date-time":"2024-11-23T03:28:38Z","timestamp":1732332518000},"source":"Crossref","is-referenced-by-count":0,"title":["Path Vertex Cover Number of Some Product Graphs"],"prefix":"10.1142","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-1754-8449","authenticated-orcid":false,"given":"Yan","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematical Science, Tianjin Normal University, Tianjin City 300071, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8423-6197","authenticated-orcid":false,"given":"Xingchao","family":"Deng","sequence":"additional","affiliation":[{"name":"College of Mathematical Science, Tianjin Normal University, Tianjin City 300071, P. R. China"},{"name":"Institute of Mathematics and Interdisciplinary Sciences, Tianjin Normal University, Tianjin City, 300071, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2024,11,22]]},"reference":[{"key":"S0219265924500221BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2011.04.008"},{"key":"S0219265924500221BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.02.024"},{"key":"S0219265924500221BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2011.09.009"},{"key":"S0219265924500221BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2011.04.023"},{"key":"S0219265924500221BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2011.09.013"},{"key":"S0219265924500221BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2011.04.009"},{"key":"S0219265924500221BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2014.03.026"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265924500221","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:24:35Z","timestamp":1746059075000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219265924500221"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,22]]},"references-count":7,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10.1142\/S0219265924500221"],"URL":"https:\/\/doi.org\/10.1142\/s0219265924500221","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"type":"print","value":"0219-2659"},{"type":"electronic","value":"1793-6713"}],"subject":[],"published":{"date-parts":[[2024,11,22]]},"article-number":"2450022"}}