Metric-locating-dominating partitions in graphs
A partition ¿ = { S 1 ,...,S k } of the vertex set of a connected graph G is a metric-locating partition of G if for every pair of vertices u,v belonging to the same part S i , d ( u,S j ) 6 = d ( v,S j ), for some other part S j . The partition dimension ß p ( G ) is the minimum cardinality of a me...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/111061 |
| Acceso en línea: | https://hdl.handle.net/2117/111061 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory dominating partition locating partition location domination metric location Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | A partition ¿ = { S 1 ,...,S k } of the vertex set of a connected graph G is a metric-locating partition of G if for every pair of vertices u,v belonging to the same part S i , d ( u,S j ) 6 = d ( v,S j ), for some other part S j . The partition dimension ß p ( G ) is the minimum cardinality of a metric- locating partition of G . A metric-locating partition ¿ is called metric-locating-dominanting if for every vertex v of G , d ( v,S j ) = 1, for some part S j of ¿. The partition metric-location-domination number ¿ p ( G ) is the minimum cardinality of a metric-locating-dominating partition of G . In this paper we show, among other results, that ß p ( G ) = ¿ p ( G ) = ß p ( G ) + 1. We also charac- terize all connected graphs of order n = 7 satisfying any of the following conditions: ¿ p ( G ) = n - 1, ¿ p ( G ) = n - 2 and ß p ( G ) = n - 2. Finally, we present some tight Nordhaus-Gaddum bounds for both the partition dimension ß ( G ) and the partition metric-location-domination number ¿ ( G ). Keywords: dominating partition, locating partition, location, domination, metric location |
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