The purpose of this paper is to find all the instances of a given set of pattern graphs (sub-graphs) in a large data graph using a single round of Map-Reduce. For the simplest pattern graphs like a triangle and rectangle we propose the solution. This paper enumerates complex pattern graphs using the enumeration of simple pattern graphs. We proposed Dominating set based graph partition, it generates non-overlapped sub-graphs. Each sub-graph is processed by one machine in the cluster. We analyze both the communication cost and the total computational cost. Communication cost is reduced by using Map-Reduce based dominating set graph partition. At the same time Multiple pattern (sub-graphs) graphs can be enumerated with the same communication cost. The proposed method is not always superior to the conventional sub-graph enumeration, but in some cases involving large-scale data where this method wins, including (1) Adjacency list representation of the graph is the input (2) Number of partitions are decided based on the graph size. We experimentally show that our approach decreases significantly the computation cost, communication cost and scales the enumeration process with a large graph database.