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Figure 7 | Journal of Cheminformatics

Figure 7

From: Efficient enumeration of monocyclic chemical graphs with given path frequencies

Figure 7

Illustration of defining the parent π ( G ) of a 1-augmented tree G . Three multi-trees T1=Gu w, T2=Gv z and T3=Gw z are obtained from G by removing a simple edge in the cycle. Each number on the left side of each vertex v in G indicates its signature σ(v) of {T w wN(v)}. The code σ for each pair of adjacent vertices in the cycle of G is given by σ(w,u)=((C,2,1),1,(C,2),1,(C,1),2,(C)), σ(u,w)=((C),2,(C,1),1,(C,2),1,(C,2,1)), σ(v,z)=((C,1),2,(C),1,(C,2,1),1,(C,2)), σ(z,v)=((C,2),1,(C,2,1),1,(C),2,(C,1)), σ(w,z)=((C,2,1),1,(C),2,(C,1),1,(C,2)), and σ(z,w)=((C,2),1,(C,1),2,(C),1,(C,2,1)). Then π(G) is defined to be T1=Gu w because σ(w,u) is maximum over all of these six codes.

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