I worked with Dr. Micheal Pawliuk at the University of Calgary on this summer research. It was about graph theory, a topic in the field of pure mathematics. The research involved two main components: understand the details of the article ``Extending partial isomorphisms of finite graphs'' (Milliet,2004) and code the algorithm presented in the article in Sage; and extend the results to a case that is unresolved. The specific theorem we worked on is ``the Hrushovski property for graphs'' or the ``Extension property for partial automorphisms (EPPA) for graphs. (Hrushovski, 1992)'