The Multibases of Symmetric Caterpillars
For a set W=w1,w2,…,wk of vertices and a vertex v of a connected graph G, the k-multiset mrvW=dv,w1,dv,w2,…,dv,wk, where dv,wi is the distance from v to wi for i=1,2,…,k, and is the multirepresentation of v with respect to W. The set W is a multiresolving set of G if the multirepresentations of ever...
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| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/5210628 |
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| author | Supachoke Isariyapalakul Varanoot Khemmani Witsarut Pho-on |
| author_facet | Supachoke Isariyapalakul Varanoot Khemmani Witsarut Pho-on |
| author_sort | Supachoke Isariyapalakul |
| collection | DOAJ |
| description | For a set W=w1,w2,…,wk of vertices and a vertex v of a connected graph G, the k-multiset mrvW=dv,w1,dv,w2,…,dv,wk, where dv,wi is the distance from v to wi for i=1,2,…,k, and is the multirepresentation of v with respect to W. The set W is a multiresolving set of G if the multirepresentations of every two distinct vertices of G with respect to W are distinct. The multiresolving set of G having the minimum cardinality is called a multibasis of G. The cardinality of a multibasis of G is the multidimensiondimMG of G. A caterpillar cak1,k2,…,ks is called a symmetric caterpillar if ki=ks−i+1 for all integers i with 1≤i≤s. In this work, the multiresolving sets of symmetric caterpillars are studied. |
| format | Article |
| id | doaj-art-392fb78cb84d44d280a4fdb48cdd2a87 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-392fb78cb84d44d280a4fdb48cdd2a872025-02-03T01:05:21ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/52106285210628The Multibases of Symmetric CaterpillarsSupachoke Isariyapalakul0Varanoot Khemmani1Witsarut Pho-on2Department of Mathematics, Srinakharinwirot University, Sukhumvit 23, Bangkok 10110, ThailandDepartment of Mathematics, Srinakharinwirot University, Sukhumvit 23, Bangkok 10110, ThailandDepartment of Mathematics, Srinakharinwirot University, Sukhumvit 23, Bangkok 10110, ThailandFor a set W=w1,w2,…,wk of vertices and a vertex v of a connected graph G, the k-multiset mrvW=dv,w1,dv,w2,…,dv,wk, where dv,wi is the distance from v to wi for i=1,2,…,k, and is the multirepresentation of v with respect to W. The set W is a multiresolving set of G if the multirepresentations of every two distinct vertices of G with respect to W are distinct. The multiresolving set of G having the minimum cardinality is called a multibasis of G. The cardinality of a multibasis of G is the multidimensiondimMG of G. A caterpillar cak1,k2,…,ks is called a symmetric caterpillar if ki=ks−i+1 for all integers i with 1≤i≤s. In this work, the multiresolving sets of symmetric caterpillars are studied.http://dx.doi.org/10.1155/2020/5210628 |
| spellingShingle | Supachoke Isariyapalakul Varanoot Khemmani Witsarut Pho-on The Multibases of Symmetric Caterpillars Journal of Mathematics |
| title | The Multibases of Symmetric Caterpillars |
| title_full | The Multibases of Symmetric Caterpillars |
| title_fullStr | The Multibases of Symmetric Caterpillars |
| title_full_unstemmed | The Multibases of Symmetric Caterpillars |
| title_short | The Multibases of Symmetric Caterpillars |
| title_sort | multibases of symmetric caterpillars |
| url | http://dx.doi.org/10.1155/2020/5210628 |
| work_keys_str_mv | AT supachokeisariyapalakul themultibasesofsymmetriccaterpillars AT varanootkhemmani themultibasesofsymmetriccaterpillars AT witsarutphoon themultibasesofsymmetriccaterpillars AT supachokeisariyapalakul multibasesofsymmetriccaterpillars AT varanootkhemmani multibasesofsymmetriccaterpillars AT witsarutphoon multibasesofsymmetriccaterpillars |