Canonical Labels for Adamantane

Starts by assigning the smallest label 1 first, and in order that the first row of the adjacency matrix is the smallest possible binary number, label 1 has to be assigned to one of the vertices having the smallest valence. In adamantane, there are six vertices having the smallest valence two, which are all symmetry equivalent. Therefore any of those can be selected and given label 1. 

The two (symmetry equivalent) adjacent vertices to vertex 1 will have labels 10 and 9, which are the largest labels that give for the first row  

FIGURE 8.3 (a) Azulene and its canonical labels, (b) The canonical spanning tree of azulene. 

FIGURE 8.4 Construction of the canonical labels for carbon skeleton of adamantane. 

Let us first recall the rules for performing the Walk Above and arriving at the Walk Above code  

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