{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:20:12Z","timestamp":1766269212286,"version":"3.41.2"},"reference-count":4,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Inter. Net."],"published-print":{"date-parts":[[2025,3]]},"abstract":"<jats:p> Let [Formula: see text] be a red\u2013white coloring of the vertices of a nontrivial connected graph [Formula: see text] with diameter [Formula: see text], where at least one vertex is colored red. Then [Formula: see text] is called an identification coloring or simply, an ID-coloring, if and only if for any two vertices [Formula: see text] and [Formula: see text], [Formula: see text], where for any vertex [Formula: see text], [Formula: see text] and [Formula: see text] is the number of red vertices at a distance [Formula: see text] from [Formula: see text]. A graph is said to be an ID-graph if it possesses an ID-coloring. If [Formula: see text] is an ID-graph, then the spectrum of [Formula: see text] is the set of all positive integers [Formula: see text] for which [Formula: see text] has an ID-coloring with [Formula: see text] red vertices. The identification number or ID-number of a graph is the smallest element in its spectrum. In this paper, we extend a result of Kono and Zhang on the identification number of grids [Formula: see text]. In particular, we give a formulation of strong ID-coloring and use it to give a sufficient condition for an ID-coloring of a graph to be extendable to an ID-coloring of the Cartesian product of a path [Formula: see text] with [Formula: see text]. Consequently, some elements of the spectrum of grids [Formula: see text] for positive integers [Formula: see text] and [Formula: see text], with [Formula: see text], are obtained. The complete spectrum of ladders [Formula: see text] is then determined using systematic constructions of ID-colorings of the ladders. <\/jats:p>","DOI":"10.1142\/s0219265924500026","type":"journal-article","created":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T15:24:46Z","timestamp":1709133886000},"source":"Crossref","is-referenced-by-count":3,"title":["On the Vertex Identification Spectra of Grids"],"prefix":"10.1142","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1958-6489","authenticated-orcid":false,"given":"Reginaldo M.","family":"Marcelo","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City 1108, Philippines"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8863-3002","authenticated-orcid":false,"given":"Mark Anthony C.","family":"Tolentino","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City 1108, Philippines"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0857-5082","authenticated-orcid":false,"given":"Agnes D.","family":"Garciano","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City 1108, Philippines"}]},{"given":"Mari-Jo P.","family":"Ruiz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City 1108, Philippines"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8457-2556","authenticated-orcid":false,"given":"Jude C.","family":"Buot","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ateneo de Manila University, Katipunan Avenue, Loyola Heights, Quezon City 1108, Philippines"}]}],"member":"219","published-online":{"date-parts":[[2024,2,28]]},"reference":[{"key":"S0219265924500026BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0219265921500055"},{"key":"S0219265924500026BIB002","doi-asserted-by":"publisher","DOI":"10.47443\/dml.2021.0042"},{"key":"S0219265924500026BIB003","first-page":"10","volume":"8","author":"Kono Y.","year":"2022","journal-title":"Discrete Math. Lett."},{"key":"S0219265924500026BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0219265921500195"}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219265924500026","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,6]],"date-time":"2025-02-06T02:13:05Z","timestamp":1738807985000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219265924500026"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,28]]},"references-count":4,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["10.1142\/S0219265924500026"],"URL":"https:\/\/doi.org\/10.1142\/s0219265924500026","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"type":"print","value":"0219-2659"},{"type":"electronic","value":"1793-6713"}],"subject":[],"published":{"date-parts":[[2024,2,28]]},"article-number":"2450002"}}