On neural networks for graph isomorphism problem

A New Algorithm for Isomorphism Determination of Undirected Graphs-Circuit Simulation Method

“…1 are isomorphic. Therefore, the degree sequence and the degree distribution sequence of G and G are the same, i.e., [3,5,4,4] and [1,1,2], respectively.…”

“…Assume that Table 2 is obtained after a comparison of all the entries in S N and S N so that S i = S i (1) (i = 1, 2, . .…”

“…Isomorphism is then determined based on the fact that the isomorphic graphs must have strict equal degree distribution sequences. Some researchers have also tried to apply neural networks to graph isomorphism determination [1,8,15,17], especially, for undirected graphs. These proposed approaches have won some achievements in the speed and accuracy of the determination, but still have low efficiency.…”

Determination of Isomorphism and Its Applications for Arbitrary Graphs Based on Circuit Simulation

“…and its eigenvalues could determine graph isomorphism [2], but this was not true either; graphs with different structures can have exactly the same characteristic polynomials and eigenvalues [1,3,[5][6][7][8][9][10][11].…”

“…According to the number in the degree sets of the vertices, we have G:[8,5,1,2,3,4,6,7] and G :[3 , 2 , 1 , 4 , 5 , 6 , 7 , 8 ]. Rearrange the adjacency matrices D and D in accordance with the position order of the vertices above.…”