Locating-Chromatic Number of Amalgamation of Stars
| Main Authors: | Asmiati, Asmiati; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa 10 Bandung., Assiyatun, H.; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa 10 Bandung., Baskoro, E. T.; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa 10 Bandung. |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
ITB Journal Publisher, LPPM ITB
, 2013
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| Subjects: | |
| Online Access: |
http://journals.itb.ac.id/index.php/jmfs/article/view/72 http://journals.itb.ac.id/index.php/jmfs/article/view/72/68 |
Daftar Isi:
- Let G be a connected graph and c a proper coloring of G . For i ƒ1,2,ƒ»,k define the color class i C as the set of vertices receiving color i . The color code c (v) „ ̈ of a vertex v in G is the ordered k -tuple 1 ( ( , ), , ( , )) k d v C ƒ» d v C where ( , ) i d v C is the distance of v to i C . If all distinct vertices of G have distinct color codes, then c is called a locating-coloring of G . The locating-chromatic number of graph G , denoted by ( ) L ƒÓ G is the smallest k such that G has a locating coloring with k colors. In this paper we discuss the locating-chromatic number of amalgamation of stars k ,m S . k ,m S is obtained from k copies of star 1,m K by identifying a leaf from each star. We also determine a sufficient condition for a connected subgraph k ,m H „~ S satisfying , ( ) ( ) L L k m ƒÓ H „T ƒÓ.