Majorization and the minimum number of dominating sets

  title={Majorization and the minimum number of dominating sets},
  author={Zdzislaw Skupien},
  journal={Discrete Applied Mathematics},
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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Showing 1-10 of 10 references

Fundamentals of Domination in Graphs

T. W. Haynes, S. T. Hedetniemi, P. J. Slater
Marcel Dekker, Inc, 1998. 302 Z. Skupień / Discrete Applied Mathematics 165 • 2014
View 1 Excerpt

Independence or domination

Z. Skupień
Positioning method in recursive counting on paths or cycles, a manuscript • 2012
View 1 Excerpt

A note on the number of dominating sets of a graph

S. Wagner
Util. Math. • 2010

Graph theory

View 1 Excerpt

Two bounds for the domination number of a graph

J. Nieminen
J. Inst. Math. Appl. 14 • 1974
View 1 Excerpt

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