Abstract
A graph γ is said to be embedded in a graph Γ if γ is isomorphic to a subgraph of Γ. The embedding frequency for γ in Γ,N( Γ, γ), is the number of different subgraphs of Γ to which γ is isomorphic. We use a computer program to calculate the embedding frequencies of subtrees within trees. We computeN(Γ, γ) for trees through 10 vertices and present the results in tabular form. When trees are partially ordered by valence class, their subtrees lie in corresponding order; we give a formal proof of this subtree embedding property. The structure of the embedding relation is exhibited in a topological picture of the zeta function showing the non-zero values ofN(Γ, γ).
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Poshusta, R.D., McHughes, M.C. Embedding frequencies of trees. J Math Chem 3, 193–215 (1989). https://doi.org/10.1007/BF01166048
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DOI: https://doi.org/10.1007/BF01166048