Let G=(V

E) be a graph

a subset DV is said to be a dominating set of G if v∈V－D， there exists u∈V such that uv∈E. The domination number of G is defined as the minimum value of |D| taken over all dominating set D of G. By the method of choosing vertex domination

some important results on domination number of a graph are obtained

some new upper bounds of domination numbers in graphs are given

and some known results are generalized.