The graph isomorphism problem asks whether two graphs are essen- tially the same. Researchers have been looking for a polynomial-time solution for it for many decades. This paper provides an algorithm for the problem using a tree-mapping approach. It converts the two graphs into trees and matches them to provide a mapping. The algorithm also ensures that the conversion and the mapping run in polynomial- time by pruning the tree appropriately as it is built. Experiments are done on the ARG Database [9][7] and the results show that all iso- morphisms for graphs with bounded degree were found in a reasonable time. As expected, the results also show that as the average degree of vertices in the graph increases so does the running time. An analysis of the algorithm indicates that the conversion and mapping both run in polynomial-time regardless of the average vertex degree of the graph.