Strong resolving graphs: the realization and the characterization problems

Identificador:  imarina:5133135

Handle: https://hdl.handle.net/20.500.11797/imarina5133135

Autors:  Kuziak, Dorota; Luz Puertas, Maria; Rodriguez-Velazquez, Juan A; Yero, Ismael G

Resum:
The strong resolving graph of a connected graph was introduced in Oellermann and Peters-Fransen (2007) as a tool to study the strong metric dimension of . Basically, it was shown that the problem of finding the strong metric dimension of can be transformed to the problem of finding the vertex cover number of . 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.