{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:44:49Z","timestamp":1760147089865,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,7]],"date-time":"2023-01-07T00:00:00Z","timestamp":1673049600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main aim of the paper is to give the crossing number of the join product G*+Dn. The connected graph G* of order six is isomorphic to K3,3\\e obtained by removing one edge from the complete bipartite graph K3,3, and the discrete graph Dn consists of n isolated vertices. The proofs were carried out with the help of several possible redrawings of the graph G* with respect to its many symmetries.<\/jats:p>","DOI":"10.3390\/sym15010175","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T02:31:30Z","timestamp":1673231490000},"page":"175","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Calculating Crossing Numbers of Graphs Using Their Redrawings"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2837-8879","authenticated-orcid":false,"given":"Michal","family":"Sta\u0161","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering and Informatics, Technical University of Ko\u0161ice, 042 00 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1137\/0604033","article-title":"Crossing number is NP-complete","volume":"4","author":"Garey","year":"1983","journal-title":"SIAM J. 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