Majorization and the minimum number of dominating sets

@article{Skupien2014MajorizationAT,
  title={Majorization and the minimum number of dominating sets},
  author={Zdzislaw Skupien},
  journal={Discrete Applied Mathematics},
  year={2014},
  volume={165},
  pages={295-302}
}
A recent Wagner result, which characterizes graphs without isolates and with a minimum number of dominating sets, is based on an earlier characterization restricted to trees. A selfcontained proof of both characterizations has been found. Each graph in question is proved to include a union of disjoint stars as a spanning subgraph which is induced by pendant edges of the graph. Majorization among numerical multisets which represent distribution of vertices among stars helps to see that the… CONTINUE READING

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