{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T01:55:19Z","timestamp":1774662919866,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Graph Theory","license":[{"start":{"date-parts":[[2019,7,30]],"date-time":"2019-07-30T00:00:00Z","timestamp":1564444800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2019,7,30]],"date-time":"2019-07-30T00:00:00Z","timestamp":1564444800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2019,7,30]],"date-time":"2019-07-30T00:00:00Z","timestamp":1564444800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>In the geodetic convexity, a set of vertices $S$ of a graph $G$ is $\\textit{convex}$ if all vertices belonging to any shortest path between two vertices of $S$ lie in $S$. The cardinality $con(G)$ of a maximum proper convex set $S$ of $G$ is the $\\textit{convexity number}$ of $G$. The $\\textit{complementary prism}$ $G\\overline{G}$ of a graph $G$ arises from the disjoint union of the graph $G$ and $\\overline{G}$ by adding the edges of a perfect matching between the corresponding vertices of $G$ and $\\overline{G}$. In this work, we we prove that the decision problem related to the convexity number is NP-complete even restricted to complementary prisms, we determine $con(G\\overline{G})$ when $G$ is disconnected or $G$ is a cograph, and we present a lower bound when $diam(G) \\neq 3$.<\/jats:p><jats:p>Comment: 10 pages, 2 figures<\/jats:p>","DOI":"10.23638\/dmtcs-21-4-4","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:54:46Z","timestamp":1743699286000},"source":"Crossref","is-referenced-by-count":1,"title":["A note on the convexity number for complementary prisms"],"prefix":"10.23638","volume":"vol. 21 no. 4","author":[{"given":"Diane","family":"Castonguay","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erika M. M.","family":"Coelho","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hebert","family":"Coelho","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julliano R.","family":"Nascimento","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2019,7,30]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1809.08220v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1809.08220v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:54:46Z","timestamp":1743699286000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/4853"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,30]]},"references-count":0,"journal-issue":{"issue":"Graph Theory","published-online":{"date-parts":[[2019,7,30]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-21-4-4","relation":{"has-preprint":[{"id-type":"arxiv","id":"1809.08220v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1809.08220v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1809.08220","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1809.08220","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"value":"1365-8050","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,30]]},"article-number":"4853"}}