I would like to read some paper, if any, for some classes of graphs, regarding inverting (right/left inverting) the incidence matrix to solve the graph isomorphism problem. Or anyway some known facts related on that problem and derived through the incidence matrix. Thank you.

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    $\begingroup$ do you mean adjacency matrix? the incidence matrix is vertex-edge matrix, not even rectangular, in general. $\endgroup$ Aug 26, 2021 at 6:26
  • $\begingroup$ I mean the incidence matrix, it is not square but can have a right or left inverse. If the incidence matrix is $A$, and $I$ the identity, there may exist $R$ and/or $L$ such that $AR=I$ or $LA=I$. $\endgroup$ Aug 26, 2021 at 6:54