PittsburghV1, France, Analysis, bibRecord, 000176

ON A GENERALIZED METRIC DIMENSION WITH PARTIALLY KNOWN GRAPH TOPOLOGY

Identifieur interne : 000176 ( France/Analysis ); précédent : 000175; suivant : 000177

ON A GENERALIZED METRIC DIMENSION WITH PARTIALLY KNOWN GRAPH TOPOLOGY

Auteurs : Sabina Zejnilovic [États-Unis] ; Dieter Mitsche [France] ; Joao Gomes [Portugal] ; Bruno Sinopoli [États-Unis]

Source :

RBID : Hal:hal-01143660

English descriptors

mix :
- graph theory.

Abstract

The metric dimension of a connected graph G is the minimum number of vertices in a subset S of the vertex set of G such that all other vertices are uniquely determined by their distances to the vertices in S. We introduce and analyze the concept of generalized metric dimension of a disconnected graph, which corresponds to the minimum number of vertices in a subset S such that all other vertices have unique distances to it in all connected graphs that result from completing a given disconnected graph. This generalization allows for incomplete knowledge of the underlying graph in applications such as identifying sources of infection. We quantify the generalized metric dimension exactly when the disconnected components are trees, cycles, grids, complete graphs and give general upper bounds on this number in terms of the boundary of the graph.

Url:

https://hal.archives-ouvertes.fr/hal-01143660

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 000423
to stream Hal, to step Curation: 000423
to stream Hal, to step Checkpoint: 000194
to stream Main, to step Merge: 000686
to stream Main, to step Curation: 000686
to stream Main, to step Exploration: 000686
to stream France, to step Extraction: 000176

Links to Exploration step

Hal:hal-01143660

Le document en format XML

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<front><div type="abstract" xml:lang="en">The metric dimension of a connected graph G is the minimum number of vertices in a subset S of the vertex set of G such that all other vertices are uniquely determined by their distances to the vertices in S. We introduce and analyze the concept of generalized metric dimension of a disconnected graph, which corresponds to the minimum number of vertices in a subset S such that all other vertices have unique distances to it in all connected graphs that result from completing a given disconnected graph. This generalization allows for incomplete knowledge of the underlying graph in applications such as identifying sources of infection. We quantify the generalized metric dimension exactly when the disconnected components are trees, cycles, grids, complete graphs and give general upper bounds on this number in terms of the boundary of the graph.</div>
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   |wiki=    Wicri/Amérique
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   |clé=     Hal:hal-01143660
   |texte=   ON A GENERALIZED METRIC DIMENSION WITH PARTIALLY KNOWN GRAPH TOPOLOGY
}}

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ON A GENERALIZED METRIC DIMENSION WITH PARTIALLY KNOWN GRAPH TOPOLOGY

ON A GENERALIZED METRIC DIMENSION WITH PARTIALLY KNOWN GRAPH TOPOLOGY

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri