Geodesic
Structure of the set of all minimal total dominating functions of some classes of graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 407-423

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In this paper we study some of the structural properties of the set of all minimal total dominating functions (_T) 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 _T(G) for some classes of graphs.
Keywords: minimal total dominating functions (MTDFs), convex combination of MTDFs, basic minimal total dominating functions (BMTDFs), simplex, polytope, simplicial complex, function separable graphs, function reducible graphs 
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     title = {Structure of the set of all minimal total dominating functions of some classes of graphs},
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Kumar, K.; MacGillivray, Gary. Structure of the set of all minimal total dominating functions of some classes of graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 407-423. http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a4/