Asmiati, Asmiati and Baskoro, Edy Tri (2012) Characterizing all graphs containing cycles with locating-chromatic number 3. Characterizing all graphs containing cycles with locating-chromatic number 3, 1 (1). pp. 351-357. ISSN 10.1063/1.4724167

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Abstract

Let G be a connected graph G. Let c be a k-coloring of V(G) which induces an ordered partition Π = {S1,S2, . . . ,Sk} of V(G), where Si is the set of vertices receiving color i. The color code cΠ(v) of vertex v is the ordered k-tuple (d(v,S1),d(v,S2), . . . ,d(v,Sk)), where d(v,Si) = min{d(v, x)|x ∈ Si}, for 1 ≤ i ≤ k. If the color codes of all vertices are different, then c is called a locating-coloring of G. The locating-chromatic number of G, denoted by χL(G) is the smallest k such that G has a locating k-coloring. In this paper, we investigate graphs with locating-chromatic number 3. In particular, we determine all maximal graphs having cycles (in terms of the number of edges) with locating-chromatic number 3. From this result, we then characterize all graphs on n vertices containing cycles with locating-chromatic number 3.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika
Depositing User: ASMIATI
Date Deposited: 25 Apr 2018 08:04
Last Modified: 25 Apr 2018 08:04
URI: http://repository.lppm.unila.ac.id/id/eprint/6726

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