Effective firefighting of major fires in fuel storage plants can effectively prevent or delay fire spread (domino effect) and eventually extinguish the fire. If the number of firefighting crew and equipment is sufficient, firefighting will include the suppression of all the burning units and cooling of all the exposed units. However, when available resources are not adequate, fire brigades would need to optimally allocate their resources by answering the question “which burning units to suppress first and which exposed units to cool first?” until more resources become available from nearby industrial plants or residential communities. The present study is an attempt to answer the foregoing question by developing a graph theoretic methodology. It has been demonstrated that suppression and cooling of units with the highest out-closeness index will result in an optimum firefighting strategy. A comparison between the outcomes of the graph theoretic approach and an approach based on influence diagram has shown the efficiency of the graph approach.