Canonical Labeling for Diamantane

One has to assign labels 1-14 to the 14 carbon atoms of diamantane so that the smallest labels have as adjacent labels with the largest numbers. This requirement will ensure that the adjacency matrix, when its rows are read from left to right and from top to bottom, results in the smallest binary number. We show below the construction of the canonical labels for diamantane. 

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In continuation, as outlined in Appendix 8, label 14 has only one site where it must go, which is also the case with label 13. The next smallest labels have two possibilities, but all the remaining labels have unique locations and could not be assigned to alternative neighboring locations. Thus, one finds that the total number of symmetry operations for diamantane, which is equal to the number of alternative labeling of vertices that will produce the same adjacency matrix, is 6 x 2 = 12. In Appendix 9, we show the 12 possible canonical labels for diamantane, and in Table 2.3, we have listed all 12 permutations of labels that leave the adjacency matrix invariant. As one... 

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