The k-Dominating Graph

@article{Haas2014TheKG,
  title={The k-Dominating Graph},
  author={R. Haas and Karen Seyffarth},
  journal={Graphs and Combinatorics},
  year={2014},
  volume={30},
  pages={609-617}
}
Given a graph G, the k-dominating graph of G, Dk(G), is defined to be the graph whose vertices correspond to the dominating sets of G that have cardinality at most k. Two vertices in Dk(G) are adjacent if and only if the corresponding dominating sets of G differ by either adding or deleting a single vertex. The graph Dk(G) aids in studying the reconfiguration problem for dominating sets. In particular, one dominating set can be reconfigured to another by a sequence of single vertex additions… CONTINUE READING
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References

Publications referenced by this paper.
SHOWING 1-10 OF 13 REFERENCES

γ–graph of a graph

K. Subramaniam, N. Sridharan
  • Bull. Kerala Math. Assoc. 5(1),
  • 2008
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Gray code numbers for graphs

  • Ars Math. Contemp.
  • 2011
VIEW 1 EXCERPT

Γ-graphs of Graphs

VIEW 3 EXCERPTS

Finding paths between 3colourings

L. Cereceda, J. van den Heuval, M. Johnson
  • J. Graph Theory 67,
  • 2010
VIEW 2 EXCERPTS

Connectedness of the graph of vertex-colourings

L. Cereceda, J. van den Heuval, M. Johnson
  • Discrete Math. 308,
  • 2008
VIEW 2 EXCERPTS