图的反符号星k控制数

设G=(V,E)是一个图,一个函数f:E→-1,+1如果∑f(e)≤0 e∈Ev]对于至少k个顶点v∈V(G)成立,则称f为图G的一个反符号星k控制函数,其中E(v)表示G中与v点相关联的边集.图G的反符号星k控制数定义为γrkss(G)=max{∑f(e) e∈E│f为图G的反符号星k控制数}。得到了一般图的反符号星k控制数的若干上界,对文6]中的结果进行了推广,还确定了路Pn和圈Cn的反符号星k控制数。

Reverse Signed Star k-subdomination Numbers of Graphs

Let G = （V, E） be a graph,a function f： E→ { -1,1} is said to be the reverse signed star k-dominating function （RSSKDF） of G if ∑e∈Eυ]f（e）≤0 holds for at least k vertices υ≤V（G）. The reverse signed star k-domination number γrss^k（G） of G is defined as γrss^k（G）=max{∑e∈Ef（e）｜f is a RSSKDF of G. In this paper, we give some upper bounds of the reverse signed star k-domination numbers of graphs, which generalize a result of 6], and determine the reverse signed star k-domination numbers of the paths Pn and cycles Cn.