On the edge dimension of a graph

@article{Zubrilina2018OnTE,
  title={On the edge dimension of a graph},
  author={Nina Zubrilina},
  journal={Discrete Mathematics},
  year={2018},
  volume={341},
  pages={2083-2088}
}
Given a connected graph G, the edge dimension, denoted edim(G), is the least size of a set S that distinguishes every edge of G, in the sense that different edges have different tuples of distances to the elements of S. The notation was introduced by Kelenc, Tratnik, and Yero, and in their paper they asked several questions. In this article we answer two of these questions: on graphs of maximal edge dimension and on a conjectured upper bound of the ratio between edim(G) and dim(G) (here dim(G… CONTINUE READING

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Uniquely identifying the edges of a graph: the edge metric dimension

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4 Excerpts

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