Distinguishing Infinite Graphs

@article{Imrich2007DistinguishingIG,
  title={Distinguishing Infinite Graphs},
  author={Wilfried Imrich and Sandi Klavzar and Vladimir Ivanovich Trofimov},
  journal={Electron. J. Comb.},
  year={2007},
  volume={14}
}
  • Wilfried Imrich, Sandi Klavzar, Vladimir Ivanovich Trofimov
  • Published 2007
  • Computer Science, Mathematics
  • Electron. J. Comb.
  • The distinguishing number $D(G)$ of a graph $G$ is the least cardinal number $\aleph$ such that $G$ has a labeling with $\aleph$ labels that is only preserved by the trivial automorphism. We show that the distinguishing number of the countable random graph is two, that tree-like graphs with not more than continuum many vertices have distinguishing number two, and determine the distinguishing number of many classes of infinite Cartesian products. For instance, $D(Q_{n}) = 2$, where $Q_{n}$ is… CONTINUE READING

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