From Graph to Molecule by Loschmidt Replacement

Within the constraints of the Loschmidt replacement, points on a graph become transformed into benzene nuclei and the connections between points are wild card variables. Molecular progeny will stem from each of the basic graph types linear, branched, cyclic, polycyclic, Platonic, and topological. 

A simple two dot picture can be transformed into a chain terminated by phenyl rings (e.g., biphenyl, tolan, or any a,co-diphenylalkane). Branching graphs transform into structures from the simple 1,3,5-triphenylbenzene to hyperbranched polymers and dendrimers. 

Loops correspond to compounds like ansa cyclophanes, but equally well they might induce the design of novel annelated benzenes. Simple and polycycles manifest the familiar classes of cyclophanes and cryptophanes commonly synthesized by practitioners of supramolecular chemistry [12,13]. The Platonic graphs are a subset of the polycyclic, but, because of their potential for high symmetry and structural simplicity, they form an especially provocative group. 

One point to keep in mind is that the goal of this discussion is to stimulate the creation of new and perhaps wonderfully complex molecular designs from relatively simple graphs. As such, a balance between the number and kind of extensions, and the variety of molecules generated, should be maintained. 

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