The Total Signed Domination Number Smaller Upper and Greatest Lower Bounds of Complete Graph
Zhang Zhong-fu · Shuxue de shijian yu renshi · 2005
Let G=G(V, E)be a graph. For a function f∶V∪E→{-1, 1},the weight of fis w(f)=∑x∈V∪Ef[x].For an element xin V∪E,we define f[x]=∑y∈N_T[x]f(y), where N_T[x]denote the set of xand the adjacent and incident elements of x∈V∪E.A total signed dominating function of Gis a function f∶V∪E→{-1, 1},such that f[x]1for all x∈V∪E.The total signed domination number γ_T(G)of Gis the minimum weight of a total signed dominating function on G.The total signed dominating function of a weight γ_T(G)we call γ_T(G)-function of G.In this paper the smaller upper and greatest lower bounds of the total signed domination number of Complete Graphare obtained.