Strong resolving graphs: the realization and the characterization problems

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URI: http://hdl.handle.net/10498/30891

DOI: 10.1016/j.dam.2017.11.013

ISSN: 0166-218X

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Author/s
Kuziak, DorotaAuthority UCA; Puertas, María Luz; Rodríguez Velázquez, J.A.; González Yero, IsmaelAuthority UCA
Date
2018-02-19
Department
Estadística e Investigación Operativa; Matemáticas
Source
Discrete Applied Mathematics - 2018, Vol. 236 pp. 270–287
Abstract
The strong resolving graph $G_{SR}$ of a connected graph $G$ was introduced in [Discrete Applied Mathematics 155 (1) (2007) 356--364] as a tool to study the strong metric dimension of $G$. Basically, it was shown that the problem of finding the strong metric dimension of $G$ can be transformed to the problem of finding the vertex cover number of $G_{SR}$. Since then, several articles on the strong metric dimension of graphs which are using this tool have been published. However, the tool itself has remained unnoticed as a properly structure. In this paper, we survey the state of knowledge on the strong resolving graphs, and also derive some new results regarding its properties.
Subjects
Strong resolving graph; strong metric dimension; graphs transformations
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional
This work is under a Creative Commons License Attribution-NonCommercial-NoDerivatives 4.0 Internacional