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I have a squared $(0,1)$ matrix. How I can know if two $(0, 1)$ matrices are the same under column and rows swapping?

Moreover, how I can characterize the equivalence classes of $(0,1)$ matrices under column and row swapping?

Maybe the question is too easy or too broad, I dont know. Anyway I would appreciate A LOT any help or bibliography for this specific question. Thank you in advance.

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  • $\begingroup$ I think if you had a nice way to answer your question, you'd also have a nice way to solve the Graph Isomorphism problem. $\endgroup$
    – Gerry Myerson
    Jun 2, 2015 at 13:06
  • $\begingroup$ @GerryMyerson, so this is a open problem? $\endgroup$
    – Masacroso
    Jun 2, 2015 at 13:14
  • $\begingroup$ Is a $(0,1)$ matrix one whose entries are either $0$ or $1$? And what exactly do you mean by column and row swapping? Do you mean transposition? $\endgroup$
    – robjohn ♦
    Jun 2, 2015 at 18:36
  • $\begingroup$ @robjohn, about 0,1: yes. About transposition... depends what you call "transposition" xD, just exchanging any column by any other column, or exchanging any row by any other row. $\endgroup$
    – Masacroso
    Jun 2, 2015 at 18:40
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    $\begingroup$ Graph Isomorphism is, for any particular pair of graphs, a finite problem, so not an open problem. What's open is whether there is any way to solve it significantly more efficiently than by a brute force search (and I think the betting among the experts is that there is no such way). More information at en.wikipedia.org/wiki/Graph_isomorphism_problem $\endgroup$
    – Gerry Myerson
    Jun 2, 2015 at 23:22

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