DOI Number : 10.5614/itbj.sci.2011.43.1.1
Hits : 18

Locating-Chromatic Number of Amalgamation of Stars

Asmiati1, H.Assiyatun & E.T. Baskoro

1Combinatorial Mathematics Research Group
FMIPA ITB
Jl. Ganesa 10 Bandung, Bandung 40132, Indonesia
Email : asmiati308@students.itb.ac.id


Abstract.

Let G be a connected graph and c a proper coloring of G. For i=1,2,,k define the color class Ci as the set of vertices receiving  color i.  The color code  cP(v) of a vertex v in G is the ordered k-tuple (d(v,C1),,d(v,Ck)) where d(v,C1) is the distance of v to Ci.  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 cL(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 Sk,m. Sk,m is obtained from k copies of star K1,m by identifying a leaf from each star. We also determine a sufficient condition for a connected subgraph H Sk,m satisfying cL(H) ≤  cL(Sk,m).



Keywords: amalgamation of stars; color code; locating-chromatic number.

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