Partition Dimension of Generalized Petersen Graph
Let G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Π is the k-vector, that is, ri|Π=di,B1,di,B2,…,di,Bk. The partition Π is called t...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/5592476 |
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| author | Hassan Raza Jia-Bao Liu Muhammad Azeem Muhammad Faisal Nadeem |
| author_facet | Hassan Raza Jia-Bao Liu Muhammad Azeem Muhammad Faisal Nadeem |
| author_sort | Hassan Raza |
| collection | DOAJ |
| description | Let G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Π is the k-vector, that is, ri|Π=di,B1,di,B2,…,di,Bk. The partition Π is called the resolving (distinguishing) partition if ri|Π≠rj|Π, for all distinct i,j∈VG. The minimum cardinality of the resolving partition is called the partition dimension, denoted as pdG. In this paper, we consider the upper bound for the partition dimension of the generalized Petersen graph in terms of the cardinalities of its partite sets. |
| format | Article |
| id | doaj-art-2f8d74fe273943829127d7d522168d02 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-2f8d74fe273943829127d7d522168d022025-02-03T06:43:52ZengWileyComplexity1099-05262021-01-01202110.1155/2021/5592476Partition Dimension of Generalized Petersen GraphHassan Raza0Jia-Bao Liu1Muhammad Azeem2Muhammad Faisal Nadeem3Business SchoolSchool of Mathematics and PhysicsDepartment of MathematicsDepartment of MathematicsLet G=VG,EG be the connected graph. For any vertex i∈VG and a subset B⊆VG, the distance between i and B is di;B=mindi,j|j∈B. The ordered k-partition of VG is Π=B1,B2,…,Bk. The representation of vertex i with respect to Π is the k-vector, that is, ri|Π=di,B1,di,B2,…,di,Bk. The partition Π is called the resolving (distinguishing) partition if ri|Π≠rj|Π, for all distinct i,j∈VG. The minimum cardinality of the resolving partition is called the partition dimension, denoted as pdG. In this paper, we consider the upper bound for the partition dimension of the generalized Petersen graph in terms of the cardinalities of its partite sets.http://dx.doi.org/10.1155/2021/5592476 |
| spellingShingle | Hassan Raza Jia-Bao Liu Muhammad Azeem Muhammad Faisal Nadeem Partition Dimension of Generalized Petersen Graph Complexity |
| title | Partition Dimension of Generalized Petersen Graph |
| title_full | Partition Dimension of Generalized Petersen Graph |
| title_fullStr | Partition Dimension of Generalized Petersen Graph |
| title_full_unstemmed | Partition Dimension of Generalized Petersen Graph |
| title_short | Partition Dimension of Generalized Petersen Graph |
| title_sort | partition dimension of generalized petersen graph |
| url | http://dx.doi.org/10.1155/2021/5592476 |
| work_keys_str_mv | AT hassanraza partitiondimensionofgeneralizedpetersengraph AT jiabaoliu partitiondimensionofgeneralizedpetersengraph AT muhammadazeem partitiondimensionofgeneralizedpetersengraph AT muhammadfaisalnadeem partitiondimensionofgeneralizedpetersengraph |