图的连通Domination数与若干不变量的联系

Relationship between Connected Domination Number and Some Invariants of a Graph

研究了图的连通控制数与全控制数、无赘数、点色数、点荫度等不变量之间的关系．将 文［２］中的一个结果ｒｃ（Ｇ）≤４ｉｒ（Ｇ）－２改进为ｒｃ（Ｇ）≤３ｉｒ（Ｇ）－２，且上界可达。

In this paper, the relationship between the connected domination number and some invariants, such as the total domination number, the irredundance number, the vertex chromatic number, together with the vertex arboricity of a graph, have been studied. Improving the inequality rc(G) ≤4ir(G)-2, we obtained rc(G)≤3ir(G)-2, and its upper limit can be achieved.