## 5 Experimental Results
These studies were carried out on a computer with Intel Core i7-10875H processor, 2.30 GHz, and 32 GB RAM._Table 8 presents the experimental results for large graphs, highlighting the performance of the MDSA on datasets of varying sizes. The table includes data on the number of nodes and edges, the size of the dominating set found (VD), and the execution time in seconds. In Table 8:  
* Random Generated Graph: The algorithm identified a dominating set of 15 nodes out of 70 nodes with 133 edges, completing the task in 0.051 s.
* dsjc500.1: For this graph with 500 nodes and 12,458 edges, MDSA found a dominating set of 23 nodes, executing in 0.091 s.
* latin_square: With 900 nodes and 307,350 edges, MDSA found a dominating set of 2 nodes, taking 0.107 s.
* flat1000_50_0: This graph contains 1000 nodes and 245,000 edges. MDSA identified a dominating set of 6 nodes in 0.175 s.
* dsjc250.5: For this graph with 250 nodes and 31,336 edges, MDSA found a dominating set of 5 nodes, executing it in 0.041 s.
* r1000.5: This graph has 1000 nodes and 238,267 edges. MDSA identified a dominating set of 5 nodes in 0.095 s.
* dsjc1000.1: For this graph containing 1000 nodes and 49,629 edges, MDSA found a dominating set of 27 nodes, executing it in 0.219 s.
* C2000.5: For this graph with 2000 nodes and 999,836 edges, MDSA identified a dominating set of 7 nodes, completing in 0.745 s.
* flat1000_60_0: This dataset has 1000 nodes and 245,830 edges, with MDSA finding a dominating set of 7 nodes in 0.204 s.
* flat1000_76_0: With 1000 nodes and 246,708 edges, MDSA found a dominating set of 6 nodes, executing it in 0.125 s.  
The experimental results demonstrate that the proposed algorithm effectively applies the principles of both the greedy search algorithm and dynamic programming. At each step, the algorithm utilizes the Malatya centrality value as the selection criterion for adding \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **CC2 FS**[44] & **FastMWDS**[25] & **RLS0**[17] & **ScBppw**[26] & **FastDS**[27] & **Our Work** \\ \hline frb45-21-5 [45] & 16 & 16 & 17 & 18 & 16 & 2 \\ frb50-23-1 [45] & 18 & 18 & 19 & 19 & 18 & 2 \\ frb50-23-2 [45] & 18 & 18 & 19 & 19 & 18 & 2 \\ frb50-23-3 [45] & 18 & 18 & 19 & 20 & 18 & 2 \\ frb50-23-4 [45] & 18 & 18 & 20 & 19 & 18 & 2 \\ frb50-23-5 [45] & 18 & 18 & 19 & 19 & 18 & 2 \\ frb53-24-1 [45] & 19 & 19 & 20 & 21 & 19 & 2 \\ frb53-24-2 [45] & 19 & 19 & 20 & 21 & 19 & 2 \\ frb53-24-3 [45] & 19 & 19 & 20 & 20 & 19 & 2 \\ frb53-24-4 [45] & 18 & 19 & 19 & 19 & 18 & 2 \\ frb53-24-5 [45] & 19 & 19 & 20 & 20 & 19 & 2 \\ frb56-25-1 [45] & 20 & 20 & 21 & 21 & 20 & 2 \\ frb56-25-2 [45] & 20 & 20 & 22 & 21 & 20 & 2 \\ frb56-25-3 [45] & 20 & 20 & 22 & 22 & 20 & 2 \\ frb56-25-4 [45] & 20 & 20 & 21 & 21 & 20 & 2 \\ frb59-26-1 [45] & 21 & 21 & 22 & 22 & 20 & 2 \\ frb59-26-2 [45] & 21 & 21 & 22 & 22 & 21 & 2 \\ frb59-26-3 [45] & 21 & 21 & 22 & 23 & 21 & 2 \\ frb59-26-4 [45] & 21 & 21 & 23 & 23 & 21 & 2 \\ frb59-26-5 [45] & 21 & 21 & 24 & 23 & 21 & 2 \\ frb100-40 [45] & 37 & 38 & 40 & 39 & 36 & 2 \\ \hline
**Average Run Time** & 96.68 s & 101.44 s & - & 95.62 s & **0.761 s** \\ \hline \hline \end{tabular} Note: Bolds are the best results for datasets.  
\end{table} 
Table 9: _Cont._a node to the dominating set. This ensures that the most central node, based on the degrees of its neighboring nodes, is consistently selected. The dynamic nature of the algorithm is evident as it recalculates the Malatya centrality values whenever a node is selected, reflecting the changes in the degrees of its neighboring nodes. This process of storing and reusing the results of subproblems allows for the algorithm to avoid unnecessary computations and maintain high efficiency. The performance metrics in our experiments show that the algorithm selects the optimal nodes efficiently, underscoring its practical applicability and effectiveness in solving the minimum dominating set problem across various graph structures and sizes.