{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T08:55:21Z","timestamp":1765356921389},"reference-count":15,"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":[[2021,3]]},"abstract":"<jats:p> A red-white coloring of a nontrivial connected graph [Formula: see text] is an assignment of red and white colors to the vertices of [Formula: see text] where at least one vertex is colored red. Associated with each vertex [Formula: see text] of [Formula: see text] is a [Formula: see text]-vector, called the code of [Formula: see text], where [Formula: see text] is the diameter of [Formula: see text] and the [Formula: see text]th coordinate of the code is the number of red vertices at distance [Formula: see text] from [Formula: see text]. A red-white coloring of [Formula: see text] for which distinct vertices have distinct codes is called an identification coloring or ID-coloring of [Formula: see text]. A graph [Formula: see text] possessing an ID-coloring is an ID-graph. The problem of determining those graphs that are ID-graphs is investigated. The minimum number of red vertices among all ID-colorings of an ID-graph [Formula: see text] is the identification number or ID-number of [Formula: see text] and is denoted by ID([Formula: see text]). It is shown that (1) a nontrivial connected graph [Formula: see text] has ID-number 1 if and only if [Formula: see text] is a path, (2) the path of order 3 is the only connected graph of diameter 2 that is an ID-graph, and (3) every positive integer [Formula: see text] different from 2 can be realized as the ID-number of some connected graph. The identification spectrum of an ID-graph [Formula: see text] is the set of all positive integers [Formula: see text] such that [Formula: see text] has an ID-coloring with exactly [Formula: see text] red vertices. Identification spectra are determined for paths and cycles. <\/jats:p>","DOI":"10.1142\/s0219265921500055","type":"journal-article","created":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T17:32:30Z","timestamp":1619112750000},"page":"2150005","source":"Crossref","is-referenced-by-count":3,"title":["Distance Vertex Identification in Graphs"],"prefix":"10.1142","volume":"21","author":[{"given":"Gary","family":"Chartrand","sequence":"first","affiliation":[{"name":"Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008-5248, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuya","family":"Kono","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008-5248, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ping","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008-5248, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,4,20]]},"reference":[{"key":"S0219265921500055BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00198-0"},{"key":"S0219265921500055BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/PL00000127"},{"key":"S0219265921500055BIB003","first-page":"349","volume":"88","author":"Chappell G. 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