Asmiati, Asmiati and Baskoro, Edy Tri (2012) Characterizing all graphs containing cycles with locatingchromatic number 3. Characterizing all graphs containing cycles with locatingchromatic number 3, 1 (1). pp. 351357. ISSN 10.1063/1.4724167

Text
Characterizing all graphs containing cycles.pdf Download (944kB)  Preview 
Abstract
Let G be a connected graph G. Let c be a kcoloring 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 ktuple (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 locatingcoloring of G. The locatingchromatic number of G, denoted by χL(G) is the smallest k such that G has a locating kcoloring. In this paper, we investigate graphs with locatingchromatic number 3. In particular, we determine all maximal graphs having cycles (in terms of the number of edges) with locatingchromatic number 3. From this result, we then characterize all graphs on n vertices containing cycles with locatingchromatic 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 
Actions (login required)
View Item 