On complete systems of invariants for small graphs

Abstract

We define a small graph to be one with n ≤ 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 other such that adjacency is preserved. An interesting algorithmic approach to graph isomorphism problem uses the “code” (sometimes called a complete system of invariants). Following this approach, two graphs are isomorphic if and only if they have the same code. We propose several complete sets of invariants to settle the GIP for small graphs. Note that no complete system of invariants for a graph is known, except for those that are equivalent to the entire adjacency matrix or list of adjacencies.

Keywords:

• Graph isomorphism problem
• complete system of invariants
• degree sequence
• cycle vector
• edge vector

C.R.Categories:

• F2.2
• G.2.2