Doubly resolvability, location and domination in graphs.

Antonio González
University of Seville

Carmen Hernando
Universitat Polit\`ecnica de Catalunya

Merc\`e Mora
Universitat Polit\`ecnica de Catalunya

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Minisymposium: METRIC DIMENSION AND RELATED PARAMETERS

Content: In this talk, we discuss several relationships among some special sets of vertices of graphs such as metric-locating-dominating sets, locating-dominating sets and doubly resolving sets. First, we extend a result of Henning and Oellermann (2004) by proving that the location-domination number of a graph is not bounded above by any polynomial function on its metric-location-domination number. However, we show that this is possible when the graph does not contain the cycles $C_4$ and $C_6$ as a subgraph. Finally, we provide a method to construct doubly resolving sets from locating-dominating sets in general graphs.

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