# 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

- MathematicsNetworks
- 1994

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.

A characterisation of universal minimal total dominating functions in trees

- MathematicsDiscret. Math.
- 1995

Total dominating functions in trees: Minimality and convexity

- MathematicsJ. Graph Theory
- 1995

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

- Political SciencePure and applied mathematics
- 1998

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

- Mathematics
- 2012

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