A characterisation of universal minimal total dominating functions in trees
type: Item
instance of: scholarly article
title: A characterisation of universal minimal total dominating functions in trees
zbMATH Open document ID: 0824.05034
DOI: 10.1016/0012-365X(93)E0192-7
author: E. J. Cockayne
author: Christina M. Mynhardt
published in: Discrete Mathematics
publication date: 1995-07-24T00:00:00Z
review text: A total dominating function (TDF) of a graph \(G= (V, E)\) is a mapping \(f\) of \(V\) into the closed interval \([0, 1]\) of real numbers with the property that for each \(v\in V\) the sum of values of \(f\) in all vertices adjacent to \(v\) is at least 1. A TDF is called minimal (MTDF), if there exists no TDF \(g\) of \(G\) with the property that \(g(x)\leq f(x)\) for all \(x\in V\) and \(g(x_ 0)< f(x_ 0)\) at least for one \(x_ 0\in V\). A convex combination of two functions \(f\), \(g\) is a function \(h_ \lambda\) given by \(h_ \lambda(x)= \lambda f(x)+ (1- \lambda) g(x)\), where \(\lambda\) is a real number from the interval \([0,1]\). If a MTDF has the property that its convex combination with any other MTDF is also a MTDF, it is called a universal MTDF. In the paper the universal minimal total dominating functions of trees are characterized.
reviewed by: Bohdan Zelinka
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 778526
zbMATH Keywords: characterization
zbMATH Keywords: minimal total dominating functions
zbMATH Keywords: total dominating function
zbMATH Keywords: TDF
zbMATH Keywords: convex combination of two functions
zbMATH Keywords: universal minimal total dominating functions
zbMATH Keywords: trees
MaRDI profile type: Publication
cites work: Universal minimal total dominating functions in graphs
cites work: Total dominating functions in trees: Minimality and convexity
cites work: Universal minimal total dominating functions of trees
cites work: Convexity of minimal total dominating functions in graphs
description: scientific article; zbMATH DE number 778526