A characterisation of universal minimal total dominating functions in trees

@article{Cockayne1995ACO,
  title={A characterisation of universal minimal total dominating functions in trees},
  author={Ernest J. Cockayne and Christina M. Mynhardt},
  journal={Discret. Math.},
  year={1995},
  volume={141},
  pages={75-84}
}
9 Citations

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References

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Universal minimal total dominating functions in graphs

TLDR
This paper is concerned with the existence of a universal MTDF in a graph, i.e., a MTDF g such that convex combinations of g and any other MTDF are themselves minimal.

Total dominating functions in trees: Minimality and convexity

TLDR
The existence in trees of a universal MTDF (i.e., an MTDF whose convex combinations with any other MTDF are also minimal) is discussed.

Convexity of minimal total dominating functions in graphs

  • Bo Yu
  • Mathematics
    J. Graph Theory
  • 1995
TLDR
A sufficient condition for an MTDF to be universal is given which generalizes previous results and is found that graphs obtained by the operation from paths, cycles, complete graphs, wheels, and caterpillar graphs have a universal MTDF.