Baskoro, Edy Tri and Asmiati, Asmiati (2013) Characterizing all trees with locating-chromatic number 3. Electronic Journal of Graph Theory and Applications, 1 (2). pp. 109-117. ISSN 2338-2287

Characterizing all trees with locating-chromatic 3.pdf

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Let c be a proper k-coloring of a connected graph G. Let � = fS1; S2; : : : ; Skg be the induced partition of V (G) by c, where Si is the partition class having all vertices with color i. The color code c�(v) of vertex v is the ordered k-tuple (d(v; S1); d(v; S2); : : : ; d(v; Sk)), where d(v; Si) = minfd(v; x)jx 2 Sig, for 1 � i � k. If all vertices of G have distinct color codes, then c is called a locating-coloring of G. The locating-chromatic number of G, denoted by �L(G), is the smallest k such that G posses a locating k-coloring. Clearly, any graph of order n � 2 has locating-chromatic number k, where 2 � k � n. Characterizing all graphs with a certain locating-chromatic number is a difficult problem. Up to now, all graphs of order n with locating chromatic number 2; n

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika
Depositing User: ASMIATI
Date Deposited: 15 Sep 2017 01:19
Last Modified: 15 Sep 2017 01:19

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