The behavior of viruses in a computer network isto attack a single node in the network and starts spreading toother nodes. Once an attack has occurred, then the main defenseagainst the attacks is to immunize the affected nodes and protectthe nodes around the infected nodes. Specific nodes are selected for immunization and thereby controlling the dissemination of viruses to more nodes in the network. This paper concentrates on node selection process in the network. For the survival of the network, immunization should take place at the optimized nodesso that further spreading should be less. There are many methods in selecting nodes from the network for immunization. Random selection of nodes, selecting nodes with priority, selecting nodes using graph reduction strategy etc are some methods in selecting a node from the network for controlling the growth of virus attack. In this paper we propose a novel way for selecting nodes from virus affected network, so that the spreading of virus can be mitigated. Dominating set of a network can be used for node selection process. Set of nodes from which any other nodes in the network can be reached is called dominating set of that network. Here we also propose an algorithm for finding dominating set from a given graph. Immunizing those nodes in the dominating set will decrease the dispersion of virus in the network.