The size of the maximum independent set (MIS) in a graph G is called the independence number. The size of the minimum connected dominating set (MIN-CDS) in G is called the connected domination number. The aim of this paper is to determine two better upper bounds of the independence number; dependent on the connected domination number for a unit ball graph. Further, we improve the upper bound to obtain the best bound with respect to the upper bounds obtained thus far.
