Abstract
In this paper, a vertex refinement method is proposed. The new vertex invariant is defined based on the number of the paths for a given length. A comparison between this vertex invariant and some other general vertex invariants has been made. It is proved that this method is as fine as other methods, and examples are given to show that this method is better than others in some case. This vertex refinement method can be used in graph isomorphism algorithms to reduce the number of mapping between the vertexes.
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