图的反符号全控制数

The Reverse Signed Total Domination Numbers of Graphs

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 reverse signed total domination number of [G]is defined as [γrstG=maxv{∑VGfv f].In this paper,we mainly study the reverse signed total domination of graphs,obtain some bounds of the reverse signed total domination numberof a graph[G],and determine the reverse signed total domination numbers of complete graphs and complete bipartite graphs.