A Small Report on Graph and Tree Isomorphism

The graph isomorphism problem consists in deciding whether two given graphs are isomorphic and thus, consists of determining whether there exists a bijective mapping from the vertices of one graph to the vertices of the second graph such that the edge adjacencies are respected. The graph isomorphism problem is a well-known open problem that was first listed as an important open problem by Karp, over three decades ago. It is something that is not inherent to graph theory in itself. When it comes to the manipulation of graphs, they are theoretical objects, their representation is not primordial, and we consider two graphs to be equal if they can be represented the same way. However, when we started doing computer-aided graph theory, this was something we could not be satisfied with, since the computer does everything with the representation, and a stricter equality is not acceptable. So we had to build algorithms as efficient as possible to test graph isomorphism. This report is a small survey on the basic algorithms and results on this isomorphism problem.