Distance-based vertex identification in graphs: The outer multiset dimension
| Autor: | Rolando Trujillo-Rasua, Yunior Ramírez-Cruz, Reynaldo Gil-Pons, Ismael G. Yero |
|---|---|
| Přispěvatelé: | Fonds National de la Recherche - FnR [sponsor], Interdisciplinary Centre for Security, Reliability and Trust (SnT) > Other [research center] |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Computer science [C05] [Engineering
computing & technology] 0209 industrial biotechnology Multiset Mathematics::Combinatorics Applied Mathematics 020206 networking & telecommunications 02 engineering and technology Sciences informatiques [C05] [Ingénierie informatique & technologie] Graph Vertex (geometry) Metric dimension Combinatorics Computational Mathematics 020901 industrial engineering & automation 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Mathematics - Combinatorics Mathematics [G03] [Physical chemical mathematical & earth Sciences] Combinatorics (math.CO) Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre] Resolving set Distance based Mathematics |
| Zdroj: | Applied Mathematics and Computation, 363, 124612. New York, Netherlands: Elsevier (2019). |
| Popis: | The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u | S ) = { | d G ( u , w 1 ) , … , d G ( u , w t ) | } . A subset of vertices S such that m ( u | S ) = m ( v | S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|