An interconnection network is a highly symmetrical connected graph of order n nodes, size m edges, connectivity κ and diameter d , where n and κ are large but m and d are small. Many interconnection networks are defined algebraically in such a way that each node has an integer value. Then every edge can be assigned the sum of the two nodes it joins. These numbers are called the edge sums of the graph. The edge sum problem of a graph is to characterize the set of edge sums. This problem was introduced by Graham and Harary who presented the solution for hypercubes. Our object is to characterize the edge sums for another family of interconnection networks, namely, deBruijn graphs.