Graph theory has played a vital role in implementation of many mathematical and computer applications [8]. The immensely critical role of graph theory calls for an efficient methodology of representing the graphs. In this paper we explore an approach to represent the graphs [1] through adjacency lists using stacks instead of the conventional methods that use linked list for creating adjacency lists [3][7]. The method discussed here is motivated by the practical requirements in terms of performance and implementation ease. We propose a new methodology to create the adjacency lists for storing the graphs through a stack [9] within an array. The array is used to store the initial vertex of every edge present in the graph. All array elements will be associated with a stack which can be used to store the end points of the edges. It provides a better mechanism of storing graphs in database as compared to the existing technique which suffers from the problem of memory allocation as it does not use the contiguous memory.