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

Reji Kumar, K.; MacGillivray, Gary

Discuss. Math., Graph Theory 30, No. 3, 407-423 (2010).

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

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