{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T17:33:48Z","timestamp":1770053628540,"version":"3.49.0"},"reference-count":3,"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":[[2026,3]]},"abstract":"<jats:p>A red\u2013white coloring of a nontrivial connected graph\u00a0[Formula: see text] is an assignment of red and white colors to the vertices of\u00a0[Formula: see text]. Associated with each vertex [Formula: see text] of\u00a0[Formula: see text] of diameter [Formula: see text] is a [Formula: see text]-vector, called the code of [Formula: see text], whose [Formula: see text]th coordinate is the number of red vertices at distance\u00a0[Formula: see text] from\u00a0[Formula: see text]. A red\u2013white coloring of\u00a0[Formula: see text] for which distinct vertices have distinct codes is called an ID-coloring of\u00a0[Formula: see text]. A pair of distinct vertices on a path of order at least 2 are called partners if they have the same eccentricity. A red\u2013white coloring of a path is called a symmetric coloring if partner vertices have the same color. In 2024, it was shown by Marcelo et\u00a0al. that any red\u2013white coloring of a path whose two leaves are red is an ID-coloring if it is not a symmetric coloring. In this paper, we prove the converse of this fact, and we use the result to establish a criterion to determine whether a red\u2013white coloring of a path is an ID-coloring or not.<\/jats:p>","DOI":"10.1142\/s021926592550001x","type":"journal-article","created":{"date-parts":[[2025,3,5]],"date-time":"2025-03-05T06:53:46Z","timestamp":1741157626000},"source":"Crossref","is-referenced-by-count":0,"title":["A Note on ID-Colorings and Symmetric Colorings of Paths"],"prefix":"10.1142","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-6520-4112","authenticated-orcid":false,"given":"Yuya","family":"Kono","sequence":"first","affiliation":[{"name":"Gakushuin Boys\u2019 Senior High School, 1-5-1 Mejiro, Toshima-ku, Tokyo, 171-0031, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,3,5]]},"reference":[{"key":"S021926592550001XBIB001","volume":"21","author":"Chartrand G.","year":"2021","journal-title":"J. Interconnection Netw."},{"key":"S021926592550001XBIB002","unstructured":"Y. Kono, Vertex Identification in Graphs. Ph.D. thesis, Western Michigan University (2022)."},{"key":"S021926592550001XBIB003","volume":"24","author":"Marcelo R.","year":"2024","journal-title":"J. Interconnection Netw."}],"container-title":["Journal of Interconnection Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021926592550001X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T07:00:07Z","timestamp":1770015607000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S021926592550001X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,5]]},"references-count":3,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["10.1142\/S021926592550001X"],"URL":"https:\/\/doi.org\/10.1142\/s021926592550001x","relation":{},"ISSN":["0219-2659","1793-6713"],"issn-type":[{"value":"0219-2659","type":"print"},{"value":"1793-6713","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,5]]},"article-number":"2550001"}}