图的反符号边全K-控制数

On Reverse Signed Edge Total k-Domination in Graphs

设G=(V,E)是一个图,一个函数f:E→{-1,+1}如果∑e′∈N(e)f(e′)≤0对于至少k条边e∈E成立,则称f为图G的一个反符号边全k控制函数。一个图G的反符号边全k控制数定义为γkst(G)=max{∑e∈Ef(e)|f为图G的反符边全k控制函数}。本文主要给出了连通图G的反符号边全k控制数γkst(G)的若干上限。

Let G=（V,E） be a graph,a function f：E→{-1,＋1} is said to be a reverse signed edge total k-dominating function（RSETk-DF） of G if ∑e′∈N（e）f（e′）≤0 holds for at least k edges e∈E（G）,the reverse signed edge total k-domination number of G is defined as γst′（G）=max{∑e∈E（G）f（e）｜f is a RSETk-DF of G}.In this paper we give some upper bounds of the reverse signed edge total k-domination number γkst（G） of a graph G.