Two Distance Domination Numbers of Graphs Resulting from Amalgamation Operation of Combination of Path Graphs and Special Graphs

The number of dominating nodes in a network that can control the surrounding linked nodes with the fewest amount of dominating nodes is known as the dominance number. In this research, the dominance number of distance two on the graph resulting from the amalgamation operation of the combination of path graphs and special graphs will be investigated. This is different from previous studies that have existed, namely both distance one and distance two domination numbers with ordinary amalgamation operations, without using a combination of path graphs and special graphs. This research emphasizes on the results of amalgamation operations of combinations of path graphs and special graphs. The method used in this research is pattern recognition and axiomatic deductive method. The results of this research are new theorems from the results of the amalgamation operation of the combination of path graphs and special graphs.