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 |
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| 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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