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              <text>Antony, Toby B.; Naduvath, Sudev</text>
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              <text>Further studies on chromatic completion of graphs</text>
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              <text>01-01-2026</text>
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              <text>Discrete Mathematics, Algorithms and Applications;Volume;18;Issue;2;Article No.;2550032;</text>
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              <text>&lt;a href="https://doi.org/10.1142/S1793830925500326" target="_blank" rel="noreferrer noopener"&gt;https://doi.org/10.1142/S1793830925500326&lt;/a&gt; &lt;br /&gt;&lt;br /&gt;&lt;a href="https://www.scopus.com/pages/publications/105008671341?origin=resultslist" target="_blank" rel="noreferrer noopener"&gt;https://www.scopus.com/pages/publications/105008671341?origin=resultslist&lt;/a&gt;</text>
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              <text>Antony T.B., Department of Mathematics, Christ University, Bangalore, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, India</text>
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              <text>The chromatic completion graph of G with respect to a proper vertex coloring c of G, denoted by Gc?, is the graph obtained by adding all possible edges to G without violating the proper coloring protocol. The maximum number of edges added to G to obtain the chromatic completion graph is the chromatic completion number ??(G). Equitable chromatic completion graph Ge? of a graph G and equitable chromatic completion number ??e(G) are the equitable analogues of Gc? and ??(G), respectively. In this paper, we present various structural aspects of chromatic completion graphs and equitable chromatic completion graphs. Also, the chromatic completion and the related parameter are described in terms of adjacency matrix and color matrix of graphs. The equitable chromatic completion graph is shown to be a Tur graph. More relevantly, we obtained the equitable chromatic completion number of an arbitrary graph G.  World Scientific Publishing Company.</text>
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              <text>chromatic completion graph; chromatic completion number; equitable chromatic completion graph; equitable chromatic completion number; Proper edge</text>
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              <text>ISSN: 17938309;</text>
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              <text>Restricted Access; Hardcopy may be available in the library</text>
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