## STRUCTURE OF THE SET OF ALL MINIMAL TOTAL DOMINATING FUNCTIONS OF SOME CLASSES OF GRAPHS

 K. Reji Kumar Department of Mathematics N.S.S College, Pandalam - 689 501, India e-mail: rkkmaths@yahoo.co.in Gary MacGillivray Department of Mathematics and Statistics University of Victoria, BC, Canada e-mail: gmacgill@math.uvic.ca

## Abstract

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.

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.

2010 Mathematics Subject Classification: Primary 05C69;
Secondary 05C35.

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