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An identity graph, sometimes also known as an asymmetric graph or rigid graph (Albertson and Collins 1996), is a graph possessing a single graph automorphism. The numbers of connected identity graphs on n=1, 2, ... nodes are 1, 0, 0, 0, 0, 8, 144, 3552, 131452, ... (OEIS A124059), with the the eight identity graphs of order six (all of which are connected) illustrated above. The numbers of identity graphs on n=1, 2, ... nodes are given by 1, 0, 0, 0, 0, 8, 152, 3696, 135004, ... (OEIS...

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