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Trees with Certain Locating-chromatic Number

Journal of Mathematical and Fundamental Sciences · Vol. 48 No. 1 (2016) · hlm. 39–47

DOI
10.5614/j.math.fund.sci.2016.48.1.4
ISSN
2338-5510, 2337-5760
Terbit
2016-04-01
Penerbit
Directorate for Research and Innovation (DRI) ITB
Bahasa
eng

Abstrak

The locating-chromatic number of a graph G can be defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are not contained in the same partition class. In this case, the coordinate of a vertex v in G is expressed in terms of the distances of v to all partition classes. This concept is a special case of the graph partition dimension notion. Previous authors have characterized all graphs of order n with locating-chromatic number either n or n-1. They also proved that there exists a tree of order n, n≥5, having locating-chromatic number k if and only if k ∈{3,4,"¦,n-2,n}. In this paper, we characterize all trees of order n with locating-chromatic number n - t, for any integers n and t, where n > t+3 and 2 ≤ t < n/2.

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15 penulis · 21 tautan kepenulisan bersama · 6 lintas organisasi

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  • Bandung Institute of Technology
  • Universitas Muhammadiyah Malang
  • Hasanuddin University
  • University of Indonesia
  • Politeknik Negeri Bandung
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  • Organisasi berbeda
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Rekan penulisOrganisasiArtikel bersama
Asmiati AsmiatiBandung Institute of Technology2
Shariefuddin; University of Kashmir PirzadaAfiliasi tidak diketahui1
Hilal A; University of Kashmir GanieAfiliasi tidak diketahui1
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

Afiliasi berasal dari OpenAlex; metadata OAI-PMH jurnal tidak memuatnya. Penulis tanpa ID OpenAlex dicocokkan berdasarkan nama, sehingga dua orang bisa tergabung atau satu orang bisa terpisah.

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">Trees with Certain Locating-chromatic Number</dc:title>
	<dc:creator>Syofyan, Dian Kastika</dc:creator>
	<dc:creator>Baskoro, Edy Tri</dc:creator>
	<dc:creator>Assiyatun, Hilda</dc:creator>
	<dc:subject xml:lang="en-US">color code</dc:subject>
	<dc:subject xml:lang="en-US">leaves</dc:subject>
	<dc:subject xml:lang="en-US">locating-chromatic number</dc:subject>
	<dc:subject xml:lang="en-US">stem</dc:subject>
	<dc:subject xml:lang="en-US">tree</dc:subject>
	<dc:description xml:lang="en-US">The locating-chromatic number of a graph G can be defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are not contained in the same partition class. In this case, the coordinate of a vertex v in G is expressed in terms of the distances of v to all partition classes. This concept is a special case of the graph partition dimension notion. Previous authors have characterized all graphs of order n with locating-chromatic number either n or n-1. They also proved that there exists a tree of order n, n≥5, having locating-chromatic number k if and only if k âˆˆ{3,4,"¦,n-2,n}. In this paper, we characterize all trees of order n with locating-chromatic number n - t, for any integers n and t, where n &amp;gt; t+3 and 2 ≤ t &amp;lt; n/2.</dc:description>
	<dc:publisher xml:lang="en-US">Directorate for Research and Innovation (DRI) ITB</dc:publisher>
	<dc:date>2016-04-01</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
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	<dc:identifier>https://journals.itb.ac.id/index.php/jmfs/article/view/1470</dc:identifier>
	<dc:identifier>10.5614/j.math.fund.sci.2016.48.1.4</dc:identifier>
	<dc:source xml:lang="en-US">Journal of Mathematical and Fundamental Sciences; Vol. 48 No. 1 (2016); 39-47</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/1470/1149</dc:relation>
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