  An effective indexing scheme for clusters that enables fast structure
comparison and congruence check is desperately desirable in the field of
mathematics, artificial intelligence, materials science, etc. Here we introduce
the concept of minimum vertex-type sequence for the indexing of clusters on
square lattice, which contains a series of integers each labeling the vertex
type of an atom. The minimum vertex-type sequence is orientation independent,
and it builds a one-to-one correspondence with the cluster. By using minimum
vertex-type sequence for structural comparison and congruence check, only one
type of data is involved, and the largest amount of data to be compared is n
pairs, n is the cluster size. In comparison with traditional coordinate-based
methods and distance-matrix methods, the minimum vertex-type sequence indexing
scheme has many other remarkable advantages. Furthermore, this indexing scheme
can be easily generalized to clusters on other high-symmetry lattices. Our work
can facilitate cluster indexing and searching in various situations, it may
inspire the search of other practical indexing schemes for handling clusters of
large sizes.
