# 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} }

- Published 2014 in Discrete Applied Mathematics
DOI:10.1016/j.dam.2013.05.002

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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