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Question:

are there any graph automorphism that imply total unimodularity of the graph's adjacency matrix,

resp. for which automorphisms exist graphs whose adjacency matrix is not totally unimodular

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  • $\begingroup$ Are your graphs oriented (or equivalently do your adjacency matrices have positive and negative entries)? $\endgroup$ Commented Aug 15 at 15:15
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    $\begingroup$ @SamHopkins the graphs are oriented $\endgroup$ Commented Aug 15 at 16:02

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