## 6 Discussion and Conclusions  
In this study, a robust method with polynomial time and space complexity is proposed, capable of producing optimal or near-optimal solutions for given graphs. The proposed algorithm, based on Malatya centrality, provides an effective solution to the minimum dominating set (MDS) problem, particularly in large-scale graphs. The algorithm efficiently identifies dominating sets with polynomial time and space complexity by integrating a greedy search strategy with dynamic programming principles. This dual approach ensures optimal or near-optimal solutions across various graph structures, making the algorithm highly versatile. Starting from the concept of first Malatya centrality, the second Malatya centrality value is calculated, and the adjacency matrix of the given graph is used at each step. The \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{3}{c}{**Our Work**} & \multicolumn{3}{c}{**Greedy [24]**} & \multicolumn{3}{c}{**CBC [24]**} & \multicolumn{3}{c}{**RLSo [17]**} \\ \cline{2-11}  & \(\text{D}_{\text{min}}\) & NR & ET(sn) & \(\text{D}_{\text{min}}\) & NR & ET(sn) & \(\text{D}_{\text{min}}\) & NR & ET(sn) & \(\text{D}_{\text{min}}\) & NR & ET(sn) \\ \hline polbooks [52] & 14 & **1** & **0.052** & 14 & 1000 & \(\approx\)36,000 & **13** & 10 & \(\approx\)36,000 & **13** & 20 & \(\approx\)600 \\ adjnoun [53] & 19 & **1** & **0.06** & **18** & 1000 & \(\approx\)36,000 & **18** & 10 & \(\approx\)36,000 & **18** & 20 & \(\approx\)600 \\ football [8] & 15 & **1** & **0.051** & 13 & 1000 & \(\approx\)36,000 & **12** & 10 & \(\approx\)36,000 & **12** & 20 & \(\approx\)600 \\ lesmis [54] & **10** & **1** & **0.061** & **10** & 1000 & \(\approx\)36,000 & **10** & 10 & \(\approx\)36,000 & **10** & 20 & \(\approx\)600 \\ netscience [53] & **349** & **1** & **0.963** & 477 & 1000 & \(\approx\)36,000 & 477 & 10 & \(\approx\)36,000 & 477 & 20 & \(\approx\)600 \\ zachary [55] & **4** & **1** & **0.04** & **4** & 1000 & \(\approx\)36,000 & **4** & 10 & \(\approx\)36,000 & **4** & 20 & \(\approx\)600 \\ celegansnevart [56] & **17** & **1** & **0.053** & 17 & 1000 & \(\approx\)36,000 & **16** & 10 & \(\approx\)36,000 & **16** & 20 & \(\approx\)600 \\ dolphins [57] & **14** & **1** & **0.035** & 15 & 1000 & \(\approx\)36,000 & **14** & 10 & \(\approx\)36,000 & **14** & 20 & \(\approx\)600 \\ hep-th [51] & **2234** & **1** & **197** & 2633 & 1000 & \(\approx\)36,000 & 2613 & 10 & \(\approx\)36,000 & 2613 & 10 & \(\approx\)3600 \\ astro-ph [51] & **2140** & **1** & **695** & 3011 & 1000 & \(\approx\)36,000 & 2930 & 10 & \(\approx\)36,000 & 2930 & 10 & \(\approx\)3600 \\ cond-mat:2003 [51] & **4744** & **1** & 4207 & 5489 & 1000 & \(\approx\)36,000 & 5379 & 10 & \(\approx\)36,000 & 5379 & 10 & \(\approx\)**3600** \\ power-US-grid [56] & **1481** & **1** & **33** & 1545 & 1000 & \(\approx\)36,000 & **1481** & 10 & \(\approx\)36,000 & **1481** & 20 & \(\approx\)600 \\ \hline \hline \end{tabular} Note: Bolds are the best results for datasets.  
\end{table} 
Table 11: The comparison results for network science. proposed algorithm is also iterative, ensuring that all algorithms have polynomial time and space complexity. Its time complexity of \(\Theta(n\times d)\) makes it particularly suitable for large datasets, where it outperforms other state-of-the-art algorithms that have higher complexities. The algorithm can work on all graphs that can be allocated by a computer within memory limits. The ability of the Malatya Dominating Set Algorithm to handle large graphs within reasonable memory and time constraints highlights its potential utility in various fields, such as wireless networks, social network analysis, and transportation planning. The innovative use of Malatya centrality values and the dynamic updating of selection criteria for nodes provide a robust framework for solving the MDS problem. The proposed algorithm was validated by applying it to various DIMACS, BHOSLIB, SNAP, and network repository datasets.