This paper studies percolation on random graphs with arbitrary degree distributions, providing exact solutions for site percolation, bond percolation, and combined site/bond percolation. The authors use generating function formalism to analyze the robustness of networks to random and targeted node or link failures. They show that networks with power-law degree distributions are highly robust to random node removal but vulnerable to targeted attacks on high-degree nodes. The percolation threshold, which marks the onset of a giant connected component, is determined by the critical occupation probability. For random node removal, the threshold is low, indicating high robustness. However, for targeted removal of high-degree nodes, the threshold is higher, showing vulnerability. The results are validated through simulations and show good agreement with theoretical predictions. The study highlights the importance of degree distribution in determining network resilience and provides insights into the robustness of real-world networks like the internet and power grids.This paper studies percolation on random graphs with arbitrary degree distributions, providing exact solutions for site percolation, bond percolation, and combined site/bond percolation. The authors use generating function formalism to analyze the robustness of networks to random and targeted node or link failures. They show that networks with power-law degree distributions are highly robust to random node removal but vulnerable to targeted attacks on high-degree nodes. The percolation threshold, which marks the onset of a giant connected component, is determined by the critical occupation probability. For random node removal, the threshold is low, indicating high robustness. However, for targeted removal of high-degree nodes, the threshold is higher, showing vulnerability. The results are validated through simulations and show good agreement with theoretical predictions. The study highlights the importance of degree distribution in determining network resilience and provides insights into the robustness of real-world networks like the internet and power grids.