图的反全符号控制数

On Reverse Total Signed Domination in Graphs

设G=(V,E)是一个非空图,对于一个函数f∶V(G)∪E(G)→{-1,1},则称f的权重为w(f)=∑x∈V(G)∪E(G)f(x)。若x∈V(G)∪E(G),定义f[x]=∑y∈NT[x]f(y)。如果对所有的x∈V(G)∪E(G)都有f[x]≤1,则称f是图G的一个反全符号控制函数。G的反全符号控制数定义为γ*rs(G)=max{w(f)|f是图G的一个反全符号控制函数}。本文得到了图的反全符号控制数的2个上界,并研究了路Pn和星图K1,n的反全符号控制数。

Let G=（V,E） be a nonempty graph,a function fV（G）∪E（G）→{-1,1},is said to be a reverse total signed domination function（RTSDF） of G if f[x]≤1 holds for each x∈V（G）∪E（G）,defining the weighing of fw（f）=∑x∈V（G）∪E（G）f（x）,f[x]=∑y∈NT[x]f（y）.The reverse total signed domination numbers γ＊rs（G） of G is defined as γ＊rs（G）=max{w（f）｜f is a RTSDF of G}.In this paper,we give some upper bounds of the reverse total signed domination numbers of graphs,and determine the reverse total signed domination numbers of paths Pn and star graph K1,n.