# A characterisation of universal minimal total dominating functions in trees

```@article{Cockayne1995ACO,
title={A characterisation of universal minimal total dominating functions in trees},
author={Ernest J. Cockayne and Christina M. Mynhardt},
journal={Discret. Math.},
year={1995},
volume={141},
pages={75-84}
}```
• Published 28 June 1995
• Mathematics
• Discret. Math.
9 Citations

### Basic Maximal Total Strong Dominating Functions

Let G = (V,E) be a simple graph. A subset D of V (G) is called a total strong dominating set of G, if for every u ∈ V (G), there exists a v ∈ D such that u and v are adjacent and deg(v) ≥ deg(u). The

### EXTREMUM AGGREGATES OF MINIMAL 0-DOMINATING FUNCTIONS OF GRAPHS

• Mathematics
• 1996
Abstract A 0-dominating function 0DF of a graph G = (V,E) is a function f: V → [0,1] such that Σ xeN(v) f(x) ≥ 1 for each ν e V with f(v) = 0. The aggregate of a 0DF f is defined by ag(f) = ΣveV f(v)

### The algorithmic complexity of certain functional variations of total domination in graphs

• Mathematics
Australas. J Comb.
• 2004
It is shown that the decision problem corresponding to the computation of the total minus domination number of a graph is NP-complete, even when restricted to bipartite graphs or chordal graphs.

### Some results on universal minimal total dominating functions

• Mathematics
• 2001
In this paper, we introduce the concepts of redundant constraint and exceptional vertex which play an important role in the characterization of universal minimal total dominating functions (universal

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

• Mathematics
Discuss. Math. Graph Theory
• 2010
It is proved that a function reducible graph is a function separable graph and the idea of function reducibility is used to study the structure of FT (G) for some classes of graphs.

### Convexity of Minimal Total Dominating Functions Of Quadratic Residue Cayley Graphs

• Mathematics
• 2012
Nathanson  paved the way for the emergence of a new class of graphs, namely,Arithmetic Graphs by introducing the concepts of Number Theory, particularly, the Theory of congruences in Graph

### Fractional Domination, Fractional Packings, and Fractional Isomorphisms of Graphs

Except where reference is made to the work of others, the work described in this dissertation is my own or was done in collaboration with my advisory committee. This dissertation does not include