Journal of Mathematical and Fundamental Sciences
Vol. 43 No. 1 (2011)

Locating-Chromatic Number of Amalgamation of Stars

Asmiati Asmiati (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa 10 Bandung.)
H. Assiyatun (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa 10 Bandung.)
E. T. Baskoro (Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa 10 Bandung.)



Article Info

Publish Date
21 Jul 2013

Abstract

Let G be a connected graph and c a proper coloring of G . For i Æ’­1,2,Æ’»,k define the color class i C as the set of vertices receiving color i . The color code c (v) "ž¨ of a vertex v in G is the ordered k -tuple 1 ( ( , ), , ( , )) k d v C Æ’» 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 "ž~ S satisfying , ( ) ( ) L L k m ƒÓ H "žT ƒÓ.

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Journal Info

Abbrev

jmfs

Publisher

Subject

Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics

Description

Journal of Mathematical and Fundamental Sciences welcomes full research articles in the area of Mathematics and Natural Sciences from the following subject areas: Astronomy, Chemistry, Earth Sciences (Geodesy, Geology, Geophysics, Oceanography, Meteorology), Life Sciences (Agriculture, Biochemistry, ...