三正则图的Upper减控制数

Upper Minus Domination Number of Three Regular Graphs

设G=(V(G),E(G))是一个三正则图,按照减控制函数的定义,将三正则图G的顶点分成若干个不交的点集,通过研究这些不交的点集之间边的关系及边的条数,证明了三正则图的U pper减控制数的一个上界Γ-(G)≤5n/8,且此上界是可达的,并构造出Γ-(G)=5n/8的一类图。

Let G=（V （G）,E （G）） be a three regular graph, by the definition of minus dominating function,its vertices of G can be separated into several disjoint sets. Considering the relationship and the number of edges between these disjoint sets ,this paper shows that the upper minus domination number of three regular graph is less than 5n/8 ,that is Г^-（G）=5n/8 and the bound is sharp. Furthermore ,this article constructs a family of three regular graph of which their upper minus dominating number is equal to 5n/8.