Abstract
The fault-tolerant resolvability is an extension of metric resolvability in graphs with several intelligent systems applications, for example, network optimization, robot navigation, and sensor networking. The graphs of convex polytopes, which are rotationally symmetric, are essential in intelligent networks due to the uniform rate of data transformation to all nodes. A resolving set is an ordered set đ of vertices of a connected graph G in which the vector of distances to the vertices in đ uniquely determines all the vertices of the graph G. The minimum cardinality of a resolving set of G is known as the metric dimension of G. If đ â Ï is also a resolving set for each Ï in đ. In that case, đ is said to be a fault-tolerant resolving set. The fault-tolerant metric dimension of G is the minimum cardinality of such a set đ. The metric dimension and the fault-tolerant metric dimension for three families of convex polytope graphs are studied. Our main results affirm that three families, as mentioned above, have constant fault-tolerant resolvability structures.
Originally published in Diskretnaya Matematika (2023) 34, â4, 108â122 (in Russian).
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On scatter properties of modular addition operation over imprimitivity systems of the translation group of the binary vector space
- On a number of particles in a marked set of cells in a general allocation scheme
- On the equality problem of finitely generated classes of exponentially-polynomial functions
- Fault-tolerant resolvability of some graphs of convex polytopes
- On bases of all closed classes of Boolean vector functions
- 10.1515/dma-2023-0018
Artikel in diesem Heft
- Frontmatter
- On scatter properties of modular addition operation over imprimitivity systems of the translation group of the binary vector space
- On a number of particles in a marked set of cells in a general allocation scheme
- On the equality problem of finitely generated classes of exponentially-polynomial functions
- Fault-tolerant resolvability of some graphs of convex polytopes
- On bases of all closed classes of Boolean vector functions
- 10.1515/dma-2023-0018