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

K. Reji Kumar; Gary MacGillivray — 2010

Discussiones Mathematicae Graph Theory

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.

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