Domination in planar graphs with small diameter

@article{Goddard2002DominationIP,
  title={Domination in planar graphs with small diameter},
  author={Wayne Goddard and Michael A. Henning},
  journal={Journal of Graph Theory},
  year={2002},
  volume={40},
  pages={1-25}
}
MacGillivray and Seyffarth (J. Graph Theory 22 (1996), 213–229) proved that planar graphs of diameter two have domination number at most three and planar graphs of diameter three have domination number at most ten. They also give examples of planar graphs of diameter four having arbitrarily large domination numbers. In this paper we improve on their results. We prove that there is in fact a unique planar graph of diameter two with domination number three, and all other planar graphs of diameter… CONTINUE READING
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