Abstract: By the way of high-order moments and the level-order computing framework,twenty kinds of node invariants were defined with the connection distance and level-order information of nodes.These node invariants reflect overall bias distribution characteristics,non-uniformity and smoothness,while the sum of squares of nodal degree reflects the distribution of the nodal degrees in the level.By comparing the number of distinguishable nodes,it is found that the sum of squares of nodal degrees obviously improves the refining ability of node invariants.The node invariants are ordered to form a vector as the graph invariant.The calculation results show that there are nine graph invariants that can distinguish between all N<25 non-isomorphic tree and N<34 non-isomorphic irreducible tree (no 2-degree tree) without instance being found so far for non-isomorphic tree with the same graph invariants for trees with more nodes.The distinguished ability of nine graph invariants to non-isomorphic graphs (N<10) exceeds the 19 results of 22 graph invariants in reference [8],and the degeneracy of nine graph invariants is small,thus improving the performance of random graph isomorphism testing.

Key words: Graph invariants, Graph isomorphism, Node invariants, Tree invariants