{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:46:44Z","timestamp":1759063604905},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:p> In a graph [Formula: see text], a vertex [Formula: see text] dominates a vertex [Formula: see text] if either [Formula: see text] or [Formula: see text] is adjacent to [Formula: see text]. A subset of vertex set [Formula: see text] that dominates all the vertices of [Formula: see text] is called a dominating set of graph [Formula: see text]. The minimum cardinality of a dominating set of [Formula: see text] is called the domination number of [Formula: see text] and is denoted by [Formula: see text]. A proper coloring of a graph [Formula: see text] is an assignment of colors to the vertices of [Formula: see text] such that any two adjacent vertices get different colors. The minimum number of colors required for a proper coloring of [Formula: see text] is called the chromatic number of [Formula: see text] and is denoted by [Formula: see text]. A dominator coloring of a graph [Formula: see text] is a proper coloring of the vertices of [Formula: see text] such that every vertex dominates all the vertices of at least one color class. The minimum number of colors required for a dominator coloring of [Formula: see text] is called the dominator chromatic number of [Formula: see text] and is denoted by [Formula: see text]. In this paper, we study the dominator chromatic number for the proper interval graphs and block graphs. We show that every proper interval graph [Formula: see text] satisfies [Formula: see text], and these bounds are sharp. For a block graph [Formula: see text], where one of the end block is of maximum size, we show that [Formula: see text]. We also characterize the block graphs with an end block of maximum size and attaining the lower bound. <\/jats:p>","DOI":"10.1142\/s1793830915500433","type":"journal-article","created":{"date-parts":[[2015,8,25]],"date-time":"2015-08-25T23:05:29Z","timestamp":1440543929000},"page":"1550043","source":"Crossref","is-referenced-by-count":6,"title":["On the dominator coloring in proper interval graphs and block graphs"],"prefix":"10.1142","volume":"07","author":[{"given":"B. S.","family":"Panda","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India"}]},{"given":"Arti","family":"Pandey","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Indian Institute of Information Technology Guwahati, Ambari, G. N. 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