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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |