More chemical signature example

A neat and tidy example of generating a structure from atoms and signatures occurred to me : adenine. It is known that this molecule forms readily from HCN under conditions similar to those thought to exist on the early Earth.

Anyway, the point is that the structure is almost exactly 6 C-N units (ignoring hydrogens and multiple bonds). A C-N is very similar to a height-1 signature, and the height-1 signatures for adenine are shown in the figure below:

Each signature (a-e) is mapped to an atom in the original structure, and then a table is shown of the maximum number of compatible bonds possible between each pair of signatures. Note that the table is not symmetric, as the compatibility operation is not commutative. Also, notice that the diagonal is not all 0 - bonds can form between atoms that both have b as a target signature.

Although these target signatures are smaller than the diameter of the adenine molecular graph, they still seem to define it completely. However, they are not guaranteed to produce only adenine as a solution - there may be other molecules with the same signature of (3a + 2b+3c+d+e).

Edit: Hmmm. That's not actually adenine, is it? In fact, it doesn't seem to be in ChEBI either. I probably should check my examples before posting them to the world.

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Adamantane, Diamantane, Twistane

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General Graph Layout : Putting the Parts Together

An essential tool for graph generation is surely the ability to draw graphs. There are, of course, many methods for doing so along with many implementations of them. This post describes one more (or perhaps an existing method - I haven't checked). Firstly, lets divide a graph up into two parts; a) the blocks, also known as ' biconnected components ', and b) trees connecting those blocks. This is illustrated in the following set of examples on 6 vertices: Trees are circled in green, and blocks in red; the vertices in the overlap between two circles are articulation points. Since all trees are planar, a graph need only have planar blocks to be planar overall. The layout then just needs to do a tree layout on the tree bits and some other layout on the embedding of the blocks. One slight wrinkle is shown by the last example in the image above. There are three parts - two blocks and a tree - just like the one to its left, but sharing a single articulation point. I had

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