Trees with Certain Locating-chromatic Number
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...
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| Language: | English |
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ITB Journal Publisher
2016-03-01
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| Series: | Journal of Mathematical and Fundamental Sciences |
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| Online Access: | http://journals.itb.ac.id/index.php/jmfs/article/view/1470 |
| _version_ | 1819230410006069248 |
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| author | Dian Kastika Syofyan Edy Tri Baskoro Hilda Assiyatun |
| author_facet | Dian Kastika Syofyan Edy Tri Baskoro Hilda Assiyatun |
| author_sort | Dian Kastika Syofyan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T11:28:37Z |
| format | Article |
| id | doaj.art-35e9dbcfcf1a45a6a0f3ccb9c83446a2 |
| institution | Directory Open Access Journal |
| issn | 2337-5760 2338-5510 |
| language | English |
| last_indexed | 2024-12-23T11:28:37Z |
| publishDate | 2016-03-01 |
| publisher | ITB Journal Publisher |
| record_format | Article |
| series | Journal of Mathematical and Fundamental Sciences |
| spelling | doaj.art-35e9dbcfcf1a45a6a0f3ccb9c83446a22022-12-21T17:48:52ZengITB Journal PublisherJournal of Mathematical and Fundamental Sciences2337-57602338-55102016-03-01481394710.5614/j.math.fund.sci.2016.48.1.4Trees with Certain Locating-chromatic NumberDian Kastika Syofyan0Edy Tri Baskoro1Hilda Assiyatun2Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, IndonesiaCombinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, IndonesiaCombinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, IndonesiaThe 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.http://journals.itb.ac.id/index.php/jmfs/article/view/1470color codeleaveslocating-chromatic numberstemtree |
| spellingShingle | Dian Kastika Syofyan Edy Tri Baskoro Hilda Assiyatun Trees with Certain Locating-chromatic Number Journal of Mathematical and Fundamental Sciences color code leaves locating-chromatic number stem tree |
| title | Trees with Certain Locating-chromatic Number |
| title_full | Trees with Certain Locating-chromatic Number |
| title_fullStr | Trees with Certain Locating-chromatic Number |
| title_full_unstemmed | Trees with Certain Locating-chromatic Number |
| title_short | Trees with Certain Locating-chromatic Number |
| title_sort | trees with certain locating chromatic number |
| topic | color code leaves locating-chromatic number stem tree |
| url | http://journals.itb.ac.id/index.php/jmfs/article/view/1470 |
| work_keys_str_mv | AT diankastikasyofyan treeswithcertainlocatingchromaticnumber AT edytribaskoro treeswithcertainlocatingchromaticnumber AT hildaassiyatun treeswithcertainlocatingchromaticnumber |