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On the bounded partition dimension of some classes of convex polytopes.
- Source :
-
Journal of Discrete Mathematical Sciences & Cryptography . Dec2022, Vol. 25 Issue 8, p2535-2548. 14p. - Publication Year :
- 2022
-
Abstract
- Let G be a connected graph with V(G) and E(G) be the vertex set and edge set. For a vertex u ∈ V(G) and a subset W ⊂ V(G), the distance between u and W is (u, W)=min {d(u, x): x ∈ W}. Let ∏ ={ W1, W2, W3, ... , Wt} be an ordered t-partition of V(G), the representation of v with respect to ∏ is the t-vector. If the representations of the all vertices of G with respect to ∏ are distinct, then t-partition ∏ is a resolving partition. The minimum t for which there is a resolving t-partition of V(G) is the partition dimension pd(G) of G. In this paper, we determined the upper bound of partition dimension for convex polytopes. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GRAPH connectivity
*POLYTOPES
Subjects
Details
- Language :
- English
- ISSN :
- 09720529
- Volume :
- 25
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Discrete Mathematical Sciences & Cryptography
- Publication Type :
- Academic Journal
- Accession number :
- 160969004
- Full Text :
- https://doi.org/10.1080/09720529.2021.1880692