On the Locating Chromatic Number of Certain Barbell Graphs
The locating chromatic number of a graph G is 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...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/5327504 |
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| author | Asmiati I. Ketut Sadha Gunce Yana Lyra Yulianti |
| author_facet | Asmiati I. Ketut Sadha Gunce Yana Lyra Yulianti |
| author_sort | Asmiati |
| collection | DOAJ |
| description | The locating chromatic number of a graph G is 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. In this paper we investigate the locating chromatic number for two families of barbell graphs. |
| format | Article |
| id | doaj-art-3d048fb1b07b4a05a21dfd52b630dfd5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3d048fb1b07b4a05a21dfd52b630dfd52025-02-03T05:58:39ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/53275045327504On the Locating Chromatic Number of Certain Barbell GraphsAsmiati0I. Ketut Sadha Gunce Yana1Lyra Yulianti2Mathematics Department, Faculty of Mathematics and Natural Sciences, Lampung University, Jl. Brodjonegoro No.1 Bandar Lampung, IndonesiaMathematics Department, Faculty of Mathematics and Natural Sciences, Lampung University, Jl. Brodjonegoro No.1 Bandar Lampung, IndonesiaMathematics Department, Faculty of Mathematics and Natural Sciences, Andalas University, Kampus UNAND Limau Manis, Padang 25163, IndonesiaThe locating chromatic number of a graph G is 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. In this paper we investigate the locating chromatic number for two families of barbell graphs.http://dx.doi.org/10.1155/2018/5327504 |
| spellingShingle | Asmiati I. Ketut Sadha Gunce Yana Lyra Yulianti On the Locating Chromatic Number of Certain Barbell Graphs International Journal of Mathematics and Mathematical Sciences |
| title | On the Locating Chromatic Number of Certain Barbell Graphs |
| title_full | On the Locating Chromatic Number of Certain Barbell Graphs |
| title_fullStr | On the Locating Chromatic Number of Certain Barbell Graphs |
| title_full_unstemmed | On the Locating Chromatic Number of Certain Barbell Graphs |
| title_short | On the Locating Chromatic Number of Certain Barbell Graphs |
| title_sort | on the locating chromatic number of certain barbell graphs |
| url | http://dx.doi.org/10.1155/2018/5327504 |
| work_keys_str_mv | AT asmiati onthelocatingchromaticnumberofcertainbarbellgraphs AT iketutsadhagunceyana onthelocatingchromaticnumberofcertainbarbellgraphs AT lyrayulianti onthelocatingchromaticnumberofcertainbarbellgraphs |