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Cuneane

While taking a look at the InChI discussion mail archives, I came across a discussion on graphs that are difficult to canonize (so called 'isospectral' graphs - I've heard the term before, but I haven't worked with eigenvalues of adjacency matrices, so did not pay them much attention).

Anyway, one such was this structure, cuneane:


which shows 3D and 2D representation of the molecule (reproduced from the wiki page), and an arbitrary numbering in the center. The three signatures A, B, and C are shown labelled by this numbering.

What's interesting about this particular example is the number of times that the same atom is represented in the signatures. For the signature called 'B', which is rooted at atom 2, the atom numbered 5 appears four times in the lowest layer of the tree. This naturally follows from the large number of rings of different sizes that make up cuneane - two 5-membered rings, two 4-membered rings, and two three-membered rings.

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