Efficient Algorithm for Dominatig Set In Graph Theory Based on Fundamental Cut-Set

Determining the minimum dominating set in connected graphs is one of most difficult problems defined as NP-hard. In this problem, it aimed to determine important nodes that can influence all via number on graph. study, an efficient near optimal algorithm showing a deterministic approach has been developed different from approximation algorithms mentioned literature for discovering set. The O(n3) time complexity determining Dominating Set (DS). At same time, original whose solution not random by using fundamental cut-set. DS consists 3 basic phases. first phase algorithm, constructs special spanning tree (Karci Max tree) graph developed. second phase, finds cut sets Kmax last Karci centrality node values are calculated with and these values, identify nodes. As result three phases, dominance calculated. detected give priority selection DS. All phases Efficient were coded R programming language results examined running sample graphs.