On The Partition Dimension of Disconnected Graphs
For a graph G=(V,E), a partition Ω=\{O_1,O_2,…,O_k \} of the vertex set V is called a resolving partition if every pair of vertices u,v∈V(G) have distinct representations under Ω. The partition dimension of G is the minimum integer k such that G has a resolving k-partition. Many results in determini...
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| Format: | Article |
| Language: | English |
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ITB Journal Publisher
2017-06-01
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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/2459 |
| _version_ | 1811257227219042304 |
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| author | Debi Oktia Haryeni Edy Tri Baskoro Suhadi Wido Saputro |
| author_facet | Debi Oktia Haryeni Edy Tri Baskoro Suhadi Wido Saputro |
| author_sort | Debi Oktia Haryeni |
| collection | DOAJ |
| description | For a graph G=(V,E), a partition Ω=\{O_1,O_2,…,O_k \} of the vertex set V is called a resolving partition if every pair of vertices u,v∈V(G) have distinct representations under Ω. The partition dimension of G is the minimum integer k such that G has a resolving k-partition. Many results in determining the partition dimension of graphs have been obtained. However, the known results are limited to connected graphs. In this study, the notion of the partition dimension of a graph is extended so that it can be applied to disconnected graphs as well. Some lower and upper bounds for the partition dimension of a disconnected graph are determined (if they are finite). In this paper, also the partition dimensions for some classes of disconnected graphs are given. |
| first_indexed | 2024-04-12T17:54:10Z |
| format | Article |
| id | doaj.art-e76caa8c5aba4375b15075e0a3b1aa27 |
| institution | Directory Open Access Journal |
| issn | 2337-5760 2338-5510 |
| language | English |
| last_indexed | 2024-04-12T17:54:10Z |
| publishDate | 2017-06-01 |
| publisher | ITB Journal Publisher |
| record_format | Article |
| series | Journal of Mathematical and Fundamental Sciences |
| spelling | doaj.art-e76caa8c5aba4375b15075e0a3b1aa272022-12-22T03:22:25ZengITB Journal PublisherJournal of Mathematical and Fundamental Sciences2337-57602338-55102017-06-01491183210.5614/j.math.fund.sci.2017.49.1.2On The Partition Dimension of Disconnected GraphsDebi Oktia Haryeni0Edy Tri Baskoro 1Suhadi Wido Saputro2Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia.Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia.Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia.For a graph G=(V,E), a partition Ω=\{O_1,O_2,…,O_k \} of the vertex set V is called a resolving partition if every pair of vertices u,v∈V(G) have distinct representations under Ω. The partition dimension of G is the minimum integer k such that G has a resolving k-partition. Many results in determining the partition dimension of graphs have been obtained. However, the known results are limited to connected graphs. In this study, the notion of the partition dimension of a graph is extended so that it can be applied to disconnected graphs as well. Some lower and upper bounds for the partition dimension of a disconnected graph are determined (if they are finite). In this paper, also the partition dimensions for some classes of disconnected graphs are given.http://journals.itb.ac.id/index.php/jmfs/article/view/2459disconnected graphdistanceforestpartition dimensionresolving partition |
| spellingShingle | Debi Oktia Haryeni Edy Tri Baskoro Suhadi Wido Saputro On The Partition Dimension of Disconnected Graphs Journal of Mathematical and Fundamental Sciences disconnected graph distance forest partition dimension resolving partition |
| title | On The Partition Dimension of Disconnected Graphs |
| title_full | On The Partition Dimension of Disconnected Graphs |
| title_fullStr | On The Partition Dimension of Disconnected Graphs |
| title_full_unstemmed | On The Partition Dimension of Disconnected Graphs |
| title_short | On The Partition Dimension of Disconnected Graphs |
| title_sort | on the partition dimension of disconnected graphs |
| topic | disconnected graph distance forest partition dimension resolving partition |
| url | http://journals.itb.ac.id/index.php/jmfs/article/view/2459 |
| work_keys_str_mv | AT debioktiaharyeni onthepartitiondimensionofdisconnectedgraphs AT edytribaskoro onthepartitiondimensionofdisconnectedgraphs AT suhadiwidosaputro onthepartitiondimensionofdisconnectedgraphs |