## 5 Experimental Results  
The experimental results will be shown on some small graphs, and the experimental results on large graphs will be shown as tabulated. **Example 1**. : _The first example is a grid \(G=(V,E)\) where \(|V|=n\). An example of a \(5\times 6\) grid graph is shown in Figure 3._  
According to the centrality values, Table 1 shows that the nodes with the potential to be selected are 2, 4, 6, 10, 21, 25, 27, and 29. In this step, the method selected node 6 and removed it from the graph. After the deletion process was completed, node 1 became a grey node and its active degree was dropped to 1. Therefore, this node was also removed from the graph. This situation is seen in Figure 4 (first step). Node 3 has the maximum \(\mathbb{V}2\) according to Table 2, and this node is selected and removed from the graph. The status of neighbors of node 3 turned grey (these are 2, 4, 8). The corresponding graph is seen in Figure 4 in the second step. The node with maximum \(\mathbb{V}2\) is 10 (Table 3), and it was selected to dominating set and node 10 was removed from the graph (the resultant graph is seen in Figure 4, third step). \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l} \hline Node \# & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline \(\overline{\Psi}_{1}\) & 1.33 & 3.25 & 2.75 & 3.25 & 1.33 & 3.25 & 4.67 & 4.33 & 4.67 & 3.25 & 2.75 & 4.33 & 4 & 4.33 & 2.75 \\ \(\overline{\Psi}_{2}\) & 0.41 & **1.44** & 0.77 & **1.44** & 0.41 & **1.44** & 1.26 & 1.13 & 1.26 & **1.44** & 0.83 & 1.15 & 0.94 & 1.15 & 0.83 \\ \hline Node \# & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25 & 26 & 27 & 28 & 29 & 30 \\ \hline \(\overline{\Psi}_{1}\) & 2.75 & 4.33 & 4 & 4.33 & 2.75 & 3.25 & 4.67 & 4.33 & 4.67 & 3.25 & 1.33 & 3.25 & 2.75 & 3.25 & 1.33 \\ \(\overline{\Psi}_{2}\) & 0.83 & 1.15 & 0.94 & 1.15 & 0.83 & **1.44** & 1.26 & 1.13 & 1.26 & **1.44** & 0.41 & **1.44** & 0.78 & **1.44** & 0.41 \\ \hline \end{tabular} Note: Bold text indicates the nodes with the highest centrality values.  
\end{table} 
Table 1: Centrality values for the first step. Figure 3: A grid of size \(5\times 6\). Table 4 illustrates that the nodes with the maximum \(\Psi\)2 are node 17 and node 19. Malatya Dominating Set Algorithm selected node 19, and it removed this node from the graph (the resultant graph is seen in Figure 4, third step). The fifth step's centrality values are seen in Table 5. Node 24 has the maximum centrality value; however, it is a grey node and its contribution to the dominating set is less than node 21 whose centrality value is 1. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l l} \hline \hline Node \# & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline \(\Psi_  
maximum amongst the white nodes. Due to this case, node 21 was selected and it was removed from the graph (the resultant graph is seen in Figure 4, fifth step). The remaining steps of the algorithm are as follows: In the sixth step, node 28 was selected and its neighbors are 23, 27, and 29. The seventh step concluded in the selection of node 12 with neighbors 7, 11, 13, and 17. The last step concluded with the selection of node 25 with neighbors 20, 24, and 30. After this step, there will be no white nodes. **Example 2**. : _This example includes the application of the Malatya Dominating Set Algorithm to Banana Tree graph._  
The centrality values are obtained when the algorithm is run on the graph seen in Figure 5, and the centrality values are seen in Table 6. The nodes with maximum centrality values are 6, 12, and 18. The algorithm selected node 6, and the resultant graph is seen in Figure 6.  
**Example 3**. : _The last step for experimental studies contains large graph applications. To this aim, there are 10 graphs that were used for experimental studies. The applications for large graphs are given in Tables 8 and 9.