2006•Journal of Central China Normal UniversityRequires access
The minus total domination number of graph
Chunxiang Wang, Jingjing Chen
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Abstract
A function f:V(G)→{-1,0,1}defined on the vertices of a graph G is a minus total domination funating function(MTDF) if the sum of its function values over any open neighborhood is at one.A MTDF f is minimal if there does not exist a MTDF g:(V(G)→){-1,0,1},f≠g,for which g(v)≤f(v) for every v∈V(G).The weight of a MTDF is the sum of its function values over all vertices.The minus total domination number of G is the minimum weight of a MTDF of G,while the upper minus total domination number of G is the maximum weight of a minimal MTDF on G.This paper studies these two parameters.In particular,it presents lower bounds on the study total domination number and upper bounds on the upper minus total domination number of a graph.