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First, select a “kink” ring (somewhere in the middle of the structure). Apply the GD algorithm to the two fragments obtained when the selected ring is erased, which will yield K1 and K2 for their respective number of Kekule´ valence structures. For the benzenoid shown in Figure 30, we obtain K1 ) 10 and K2 ) 17. Now erase all rings linearly fused to the “kink” ring and apply the GD algorithm to these smaller two fragments, which will yield k1 and k2 for their respective number of Kekule´ valence structures.

433 A few minutes suffice to draw the four unexcited structures for anthracene, the five for phenanthrene or the six for pyrene ... an hour or two might be needed for the 110 structures of tetrabenzoheptacene. Finding K for benzenoid hydrocarbons having a dozen fused rings requires more efficient schemes. A simple graph theoretical algorithm for construction of Kekule´ valence structures is as follows:437 (1) (2) (3) (4) (5) Construct two copies of the molecular diagram. Select a CC bond and assign to it CC double and CC single bond type in each of the copies, respectively.

103, No. 9 Figure 44. 505 to represent degenerate rearrangement of C2H5+, known as the DesarguesLevi graph. ity, which can be pictured in different geometrical ways. Planarity of a graph and planarity of a molecule are therefore different things. For example, all Platonic polyhedra are 3-D objects; hence, in a geometrical sense they are non-planar, but their graphs (which can be depicted also as Schlegel projections) are planar. 505 It is known as the Desargues-Levi graph (Figure 44) and represents degenerate rearrangements of the C2H5+ carbonium ion via multiple 1,2-shifts.

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