## Structure of the set of all minimal total dominating functions of some classes of graphs.(English)Zbl 1217.05183

Summary: We study some of the structural properties of the set of all minimal total dominating functions $$({\mathfrak F}_T)$$ 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 $${\mathfrak F}_T(G)$$ for some classes of graphs.

### MSC:

 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C35 Extremal problems in graph theory
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