ON COMPLETE SYSTEMS OF INVARIANTS FOR SMALL GRAPHS

We define a small graph to be one with n less than or equal to 6 nodes . The celebrated Graph Isomorphism Problem (GIP) consists in deciding whether or not two given graphs are isomorphic, i.e., whether there is a bijective mapping from the nodes of one graph onto those of the oth er such that adjacency is preserved. An interesting algorithmic approa ch to graph isomorphism problem uses the ''code'' (sometimes called a complete system of invariants). Following this approach, two graphs ar e isomorphic if and only if they have the same code. We propose severa l complete sets of invariants to settle the GIP for small graphs. Note that no complete system of invariants for a graph is known, except fo r those that are equivalent to the entire adjacency matrix or list of adjacencies.