A New Method for Finding an Improved Bound on the Maximal Independent Set and Minimal Connected Dominating Set in the Unit Ball Grph

A New Method for Finding an Improved Bound on the Maximal Independent Set and Minimal Connected Dominating Set in the Unit Ball Grph Abstract The size of maximum independent set in a graph G is called the independence number. The size of the minimum connected dominating set in G is called the connected domination number. The independent number denoted by α(G) and the connected domination number denoted by γ_c (G). In other hand relation between the size of the maximal independent set and the size of the minimal connected dominating set in a graph G is very important. 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. Keywords: Connected dominating set, Independent number, Unit ball graph, Maximal independent set, Connected domination number.