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Locating-Chromatic Number of Amalgamation of Stars

Journal of Mathematical and Fundamental Sciences · Vol. 43 No. 1 (2013) · hlm. 1–8

DOI
10.5614/itbj.sci.2011.43.1.1
ISSN
2338-5510, 2337-5760
Terbit
2013-07-21
Penerbit
Directorate for Research and Innovation (DRI) ITB
Bahasa
eng

Abstrak

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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  • Bandung Institute of Technology
  • Universitas Jambi
  • Lampung University
  • Indonesian National Institute of Aeronautics and Space
  • Universitas Muhammadiyah Malang
  • Hasanuddin University
  • University of Indonesia
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Rekan penulisOrganisasiArtikel bersama
Dian Kastika SyofyanBandung Institute of Technology2
Rachmawati RachmawatiUniversitas Jambi1
Damris MuhammadUniversitas Jambi1
Shariefuddin; University of Kashmir PirzadaAfiliasi tidak diketahui1
Hilal A; University of Kashmir GanieAfiliasi tidak diketahui1
Aang NuryamanLampung University1
Muhammad Ihsan AbyanLampung University1
Bagus Hayatul JihadIndonesian National Institute of Aeronautics and Space1
Soleh Fajar JunjunanIndonesian National Institute of Aeronautics and Space1
A.N.M. SalmanBandung Institute of Technology1
Hajo J. BroersmaBandung Institute of Technology1
Yus Mochamad CholilyUniversitas Muhammadiyah Malang1
Nurdin NurdinHasanuddin University1
Muhammad Kamran SiddiquiAfiliasi tidak diketahui1
Denny Riama SilabanUniversity of Indonesia1
Saladin UttunggadewaBandung Institute of Technology1
Anie LusianiPoliteknik Negeri Bandung1
Suhadi Wido SaputroBandung Institute of Technology1

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Sumber metadata: OAI-PMH (metadata jurnal) https://journals.itb.ac.id/index.php/jmfs/oai, pertama di-harvest 9 Nov 2026, terakhir terlihat 9 Nov 2026.
Metadata asli (oai_dc) 
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	<dc:title xml:lang="en-US">Locating-Chromatic Number of Amalgamation of Stars</dc:title>
	<dc:creator>Asmiati, Asmiati</dc:creator>
	<dc:creator>Assiyatun, H.</dc:creator>
	<dc:creator>Baskoro, E. T.</dc:creator>
	<dc:description xml:lang="en-US">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.</dc:description>
	<dc:publisher xml:lang="en-US">Directorate for Research and Innovation (DRI) ITB</dc:publisher>
	<dc:date>2013-07-21</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journals.itb.ac.id/index.php/jmfs/article/view/72</dc:identifier>
	<dc:identifier>10.5614/itbj.sci.2011.43.1.1</dc:identifier>
	<dc:source xml:lang="en-US">Journal of Mathematical and Fundamental Sciences; Vol. 43 No. 1 (2011); 1-8</dc:source>
	<dc:source>2338-5510</dc:source>
	<dc:source>2337-5760</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://journals.itb.ac.id/index.php/jmfs/article/view/72/68</dc:relation>
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