Structure of the set of all minimal total dominating functions of some classes of graphs

@article{Kumar2010StructureOT,
  title={Structure of the set of all minimal total dominating functions of some classes of graphs},
  author={K. Kumar and Gary MacGillivray},
  journal={Discuss. Math. Graph Theory},
  year={2010},
  volume={30},
  pages={407-423}
}
In this paper we study some of the structural properties of the set of all minimal total dominating functions (FT ) of cycles and paths and introduce the idea of function reducible graphs and function separable graphs. It is proved that a function reducible graph is a function separable graph. We shall also see how the idea of function reducibility is used to study the structure of FT (G) for some classes of graphs. 
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References

SHOWING 1-10 OF 14 REFERENCES
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.
Fundamentals of domination in graphs
Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of
Graph Theory: An Introductory Course
TLDR
In an elementary text book, the reader gains an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject.
A characterization of universal minimal total dominating functions in trees, Discrete Math
  • A characterization of universal minimal total dominating functions in trees, Discrete Math
  • 1995
Structure of the Set of All Minimal Total Dominating
  • Structure of the Set of All Minimal Total Dominating
Mynhardt, A characterization of universal minimal total dominating functions in trees
  • Discrete Math
  • 1995
Topological properties of the set of all minimal total dominating functions of a graph
  • Topological properties of the set of all minimal total dominating functions of a graph
...
...