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In short, I found an algorithm for GI and the only hard instances I found so far are non-isomorphic strongly regular graphs with large automorphism groups. Q1 What are hard instances for the ...

This is related to graph isomorphism. Here matrices are square $n \times n$ with non-negative integer entries. Two matrices $A,B$ are permutation similar if there exist permutation matrix $P$ such ...

$\DeclareMathOperator\ora{ora}$Let $A_0$ be the adjacency matrix of graph $G$ and $P_0$ permutation matrix of multiplicative order $\rho$. Let $X$ be positive integer and $B_0=P_0^X A_0 P_0^{-X}$. Q1 ...

Roughly speaking, we are trying to find complete graph invariant as the lexicographically first matrix from the permutations of the adjacency matrix. Let $G$ be graph, possibly directed graph, of ...