图的反符号全控制数

摘要

设G=(V,E)是一个无孤立顶点的图,一个函数f:V→{-1,+1｝称为图G的一个反符号全控制函数,如果f(N(v))≤1对任何点v∈V(G)成立.图G的反符号全控制数记为γrst(G)=max{f(V)｜f为图G的一个反符号全控制函数｝.该文对图的反符号全控制函数进行了研究,获得了一般图的反符号全控制数的若干界限,确定了完全图和完全二部图的反符号全控制数.%Let G=(V,E) be a graph without islate vertex, a function f.V→[-1, 1} is said to be the reverse signed total dominating function (RSTDF) of G if ∑ v∈N(u)f(v)≤ 1 holds for every vertex u ∈ V(G). The reversesigned total domination number γrsr(G) of G is defined as γrst(G) =max{∑v∈v(G)f(v) |f is an RSTDF of G}. In this paper,we mainly study the reverse signed total domination of graphs, obtain some bounds of the reverse signed total domination number γrst(G) of a graph G , and determine the reverse signed total domination numbers of complete graphs and complete bipartite graphs.