定义在图G上的一个函数f:V(G)→{-1,0,1},如果在任何一点的开领域的权和至少为1,则称f是一个全负控制函数(简记为(MTDF).对一个全负控制函数f而言,如果不存在一个全负控制函数g:V(G)→{-1,0,1},f≠g,对每个点v∈V(G),有g(v)≤f(v),则称f是极小的.一个MTDF f 的权是指其所有点函数值的总和.图G的全负控制数是G的极小MTDF的最小权,而图G的上全负控制数是G的极小MTDF的最大权.本文主要研究这两个参数,得到它们的一些界的结论.
摘要(英文):
A function f:V(G)→{ -1,0,1 }defined on the vertices of a graph G is a minus total domination funating function (MTDF) if the sum of its function values over any open neighborhood is at one. A MTDF f is minimal if there does not exist a MTDF g: V(G)→{-1,0,1} ,f≠g,for which g(v)≤f(v) for every v∈V(G). The weight of a MTDF is the sum of its function values over all vertices. The minus total domination number of G is the minimum weight of a MTDF of G, while the upper minus total domination number of G is the maximum weight of a m...